When 5 million tourists annually -- meaning five times its population -- visit a city, it obviously has quite a bit going for it. And that's Cologne.

Testimonials to the town, fourth largest in Germany after Berlin, Hamburg and Munich, certainly abound.

Petrarch, who visited in the 14th century when the city was already 1,300 years old, sang praises of its civilized ways and expressed surprise that "an urban center of such beauty" even existed in a land that he otherwise described as "barbarian."

Victor Hugo, the novelist and dramatist, went Petrarch one better. He described himself as the "barbarian" when he first saw "this admirable city, a city of dreams," in the 19th century: a remarkable concession to the Germans from a Frenchman.

And Heinrich Bo ll, the Nobel laureate, a usually caustic critic of the town in which he was born and continues to live, is on record as saying: "Of all Germany's cities, it was the one in which Adolf Hitler felt the least comfortable. In no other did he let himself be seen as rarely. That says a lot for Cologne, its spirit and its people."

What is it that draws the crowds? Certainly that majestic Gothic cathedral, one of the largest in Christendom, and naturally the Rhine, that West European artery from whose banks Cologne rises like a vast citadel. And when one mentions Cologne, what else comes to mind besides some of the great figures of history, art, literature, music and science -- Albertus Magnus, Thomas Aquinas, Marie de Medici, Peter Paul Rubens, Georg Simon Ohm or Max Bruch -- who at one time or another called it home? No doubt the scented toilet water that bears the name of the city in which it was invented some 275 years ago and is still produced.

But there's more: Call it Cologne's "four C's" -- carnival, churches, culture and commerce. There is no required order to the sequence. It's a matter of personal preference and the seasons.

The commerce dates back nearly 2,000 years. It contributed to Cologne becoming a key member of the medieval Hanseatic League of trading cities, and because of the spate of trade fairs -- at least one a month -- it still makes finding hotel rooms a problem.

The carnival season is for Cologne what Mardi Gras is to New Orleans, an explosion of reveling that culminates in the annual Rose Monday parade and the boistrous Shrove Tuesday festivities. That being over for this year, it seems appropriate to turn to the churches, by which Ko lner (as the locals are called) for once do not mean that cathedral whose twin spires tower trademark-like 520 feet above the Rhine. Seldom at a loss for a reason to celebrate or commemorate, they have designated 1985 as the "Year of the Romanesque Churches."

Forty years after the end of World War II, which left them and 90 percent of Cologne's historic Old City a pile of smoldering rubble, 12 of these splendid medieval edifices are again open to worshippers and visitors, having been finally restored and renovated by Cologne's Roman Catholic archdiocese and the city, state and federal governments at a cost of more than $80 million.

All make the famed cathedral seem like an architectural adolescent. Some of them -- St. Gereon's is an example -- incorporate foundations, crypts, walls and pillars that date from the 4th to 6th centuries. The oldest, St. Pantaleon's, a former Benedictine abbey, was consecrated in 980. The youngest, St. Kunibert's, a collegiate church, was completed in 1247, one year before Archbishop Konrad von Hochstaden, Cologne's spiritual and temporal ruler, laid the cornerstone to the cathedral.

In fact, these monuments of the Middle Ages, now again crammed with priceless works of arts, were Cologne's distinguishing features for more than half a millennium, and their massive, unadorned, fortress-like towers and turrets formed the city's distinctive skyline long before the cathedral's own filigreed, neo-Gothic spires went up in the 19th century during Germany's age of romanticism.

All are within walking distance of each other and all but one, St. Cecilia's -- which houses the Schnu tgen Museum, a stunning collection of sacral art from the Carolignian through the Baroque eras -- are used for services.

Visitors interested in seeing all 12 churches are advised that the city tourist office is offering guided, English-language four-day tours, which can be shortened or varied and expanded to include other sights. In addition, throughout the year there will be a spate of festive masses, special ecclesiastical art exhibitions at the Schnu tgen and Haubrich-Kunsthalle museums, lectures, symposiums, concerts and opera performances. The operatic highlight will be the May 31 premiere of a revival production of Georg Friedrich Handel's long-forgotten early work, "Agrippina," first performed in Venice in 1709.

The choice of that particular opera to commemorate the Handel Tricentennical in Cologne is not coincidence. It was Agrippina, the scheming great-granddaughter of Augustus Caesar, daughter of Germanicus, sister of Caligula, niece as well as wife of Emperor Claudius and mother of Nero, who really put Cologne on the map. She was born there in A.D. 15.

The story of her incestuous intrigues, which makes for a hot plot despite the musically slow-moving, recitative nature of Handel's early operas, also focuses on a vital fact. For all its preoccupation with things Romanesque and medieval this year, what is really important about Cologne is its Roman origin.

It was Agrippina's grandfather, Marcus Vispanius Agrippa, general and admiral, Augustus' most trusted lieutenant and architect of his victory over Antony and Cleopatra, who founded the town in 38 B.C. as a Roman garrison and settlement of the friendly Ubii tribe, naming it "Oppidium Ubiorum."

For the next eight decades or so it grew in importance as a river port and military outpost, with a succession of Roman generals and aristocrats encamping in the town en route to other far-flung points of the empire along the Rhine and in the Low Countries -- including, of course, Germanicus and his wife, Agrippina the Elder, who gave birth to their daughter there.

In the year 28, at age 13, this tempestuous offspring married the first time and had a son: Nero of later fiddle-and-fire fame. The marriage broke up, as did a second one. But then, in 48 A.D., she married Emperor Claudius, her widowed uncle 25 years her senior. Two years later Agrippina prevailed on him to elevate her home town to a full-fledged city and colony: "Colonia Claudia Ara Agrippinensis." Over the succeeding centuries that tongue-twisting name was conveniently shortened, it being more expedient even in Latin to just say "Colonia," which the Germans eventually turned into Ko ln and the French and English into Cologne.

The city is infamous for its klu ngel -- the moneyed in-crowd cliques whose intrigues are immortalized in many a novel and play. Locals say it all began with little Agrippina, and that Handel's opera really tells it as it was. She dominated her aging third husband and manipulated him into advancing the interests of her first-born, Nero, at the expense of his own son, Brittanicus. She quarreled with Seneca, with Narcissus and with just about every other official in Rome. Finally, after six years of marriage, which must have been a nightmare for him, she poisoned Claudius and put Nero on the throne. Weary of his mother's scheming, he rewarded her by murdering her five years later.

After these tumultuous years, Cologne settled into a more tranquil era of growth and prosperity, becoming the provincial capital of Lower Germany and one of the largest, most affluent cities of the Roman empire, with splendid palaces, temples, villas and stone bridges across the Rhine -- until Rome itself collapsed under pressure from the Germanic barbarians who conquered and sacked Cologne for the first of several times in 355.

To be sure, Christianity had rather early roots there: the 2nd century A.D., to judge from tombstones found near the Schnu tgen Museum, and the first mention of a Cologne bishop, Maternus, was in 313 when he participated at a council in the Lateran. But the Dark Ages were especially dark in the city, including its conquest and destruction by the Normans in 881. It was really not until the 10th century that Cologne began blossoming as one of the great ecclesiastical, urban and mercantile centers of medieval Germany, joining the Hanseatic League in 1250, founding a university in 1388 and becoming a Free City of the German Reich, with the right of coinage, in 1475.

The period of glory ended in 1794 with Cologne's occupation and amalgamation by France during the French Revolutionary War. It remained French until Napoleon's defeat in 1815, then became Prussian, which the Ko lner hated even more. The Prussian takeover was something they never forgot nor forgave, and contributed to their later attitude toward Hitler. Indeed, though World War II devastated their town, more than just a few in Cologne also regarded it as a blessing in disguise; not only did it finish Hitler's Third Reich, but it sealed the fate of Prussia, which no longer exists as a state.

To this day the Prussian legacy determines Heinrich Bo ll's feelings about Cologne's cathedral. "I like its interiors," he says, "but not the outside. The Prussians finished the building, particularly the spires, in the 19th century and imbued it with all their patriotic garbage. The spires are horribly Hohenzollern."

Another Ko lner with a long memory and hatreds was Konrad Adenauer, the mayor from 1917 until he was ousted by the Nazis in 1933. Legend has it that in the 1920s he wanted to secede even from republican Weimar Germany and create a separatist Rhineland state with Cologne as its capital. Adenauer's anti-Prussianism, some locals say with a smile as sly as his, may also have contributed to his eagerness (as postwar West Germany's first chancellor) to make Bonn, 15 miles upstream, the capital, reconcile with France, join the Western alliance and leave Prussia to those who rule its dismembered parts today -- the Russians, the Poles and the East Germans.

Legends abound in Cologne and invariably confront visitors. One centers on the church of St. Gereon, named for a martyred centurion of Rome's Thebian Legion, one of the empire's military pillars in the Rhineland during the reign of coemperors Diocletian and Maximian. Having been recruited in Egyptian Thebes, where their parents and grandparents had long been Christian, these soldiers refused to pray to the Jovian gods. In 290 Maximian construed this as disloyalty to Rome and ordered them executed. Gereon, stationed in Cologne, was the most steadfast and defiant in adherence to his faith. His corpse and those of his men were allegedly thrown into a well near the city wall. Local Christians sanctified the spot. Several decades later, after Constantine the Great's conversion to Christianity, Helena, the emperor's devout mother, commissioned the building of a beautiful church on the site: St. Gereon's.

Stirring as the tale sounds, it has failed to pass the tests of archeological excavation and written history. Digs have turned up no trace of the well and St. Helena died in 328, more than 50 years before construction began on what is today the basilica of St. Gereon.

But then, Ko lner do not let facts stand in the way of a good yarn -- a policy that is good for business. St. Ursula, the city's patron saint, is a radiant example of that.

She was an English princess, so the legend goes, and a virgin, devoted to God. When, for reasons of realpolitik, her father promised her to Aetherius, a handsome young prince from a powerful foreign land -- but alas a heathen -- she put down her pious, maidenly foot and set conditions. Aetherius would have to wait three years, during which she expected him to convert to Christianity. Meanwhile she would make a pilgrimage to Rome, accompanied by 11,000 other virgins, aboard 11 ships which, naturally, papa's naval yard would build.

Ultimately off she sailed, across the Channel to what is now Rotterdam, and up the Rhine to Basel. From there it was overland to Rome, an audience with the Pope, and back to Basel, where she and her entourage reembarked, joined by young Aetherius who had since indeed converted. When they reached Cologne they were waylaid by Huns, then besieging the city, and in a fashion most cruel, all were slaughtered. The horror of this deed brought the angels to the side of Cologne's defenders who, miraculously, were able to turn the tide of battle and force the Huns to flee. Devout Ko lner buried the martyred maidens, added 11 little flames, each representing 1,000 virgins, to the city's coat of arms, and built a church, St. Ursula's, on the burial site.

It happened, so the tale says, in 238, and like every legend this one also has some grains of truth. There is evidence of a Christian massacre in 3rd-century Cologne, and excavations at St. Ursula's (one of the 12 Romanesque churches) revealed the foundations of a 4th-century chapel. At any rate, over eons the story got better and bigger, leading to an Ursula cult.

In the early 1100s, when ground was broken for the present church, workmen chanced upon a large cemetery, probably Roman or Frankish, containing many remains. Ursula and her followers? Who else?

The bones were gathered as relics. Many were enshrined in intricately carved and exquisitely painted busts of young women and sold all over Europe, putting Cologne into the reliquary trade. Thousands of the bare bones and scores of the carved wooden heads line the walls of St. Ursula's "Golden Chamber" (a room in the chapel decorated with gold-leaf ornaments) today.

Relics also have made Cologne a magnet for pilgrims and tourists -- especially the remains of the Three Wise Men for whom the cathedral was built. Again Helena plays a legendary role, allegedly having found the relics in Asia and brought them to Constantinople. In the Dark Ages, the relics were carried from there to Milan Cathedral. In 1164 Reinald von Dassel, who was both archbishop of Cologne and chancellor to Emperor Frederick Barbarossa, filched them from Milan and took them to Cologne. A dazzling golden shrine was cast for them and plans drawn for a grand new temple, the largest in all Christendom, to house it.

More than 80 years passed before construction began, and another 632 until those Prussians placed the last flowery finial atop one of the spires in 1880. But the glittering shrine of the Magi soon became, and has remained until today, the cathedral's most sacred and artistically stunning sight.

Besides the cathedral and the Romanesque churches, only a few architectural treasures from Cologne's medieval past survived the air raids or were rebuilt. Among them are the opulently decorated Gothic and Renaissance Rathaus, the city hall; the Gu rzenich, a 15th-century banquet and meeting hall; the Overstolzenhaus, a 13th-century Romanesque patrician mansion that is now the Arts and Crafts Museum; the 4711 House, home of one of the original toilet-water distilleries; and the totally reconstructed little district of narrow lanes, cobblestone streets and gabled houses between the Romanesque church of Gross St. Martin and the Rhine embankment -- though with its profusion of taverns, nightclubs and mediocre restaurants, the area is Disneylandish and somewhat of a tourist trap.

Fortunately, the bombs did not destroy underground Cologne -- the Roman city. Indeed, they helped in its discovery. The Praetorium, the Roman governor's palace -- a huge, 360,000-square-foot complex -- was not found until 1953, when workmen began clearing rubble and digging foundations for an annex to the city hall. The same is true of the ancient Jewish ritual bath, adjacent to the Praetorium, and of Roman streets and pipelines that honeycomb subterranean Cologne.

One of the city's greatest Roman treasures is the magnificent and nearly pristine Dionysius Mosaic, laid between A.D. 260 and 280 as the dining room floor of a wealthy merchant's villa. It was discovered only in 1941 during the construction of an air-raid shelter. Still in its original location, just south of the cathedral, it is now surrounded by the fabulous Roman-Germanic Museum.

Another of the museum's riches is the tomb of Lucius Poblicus, a 1st-century centurion. The 45-foot-high monument was found in 1965 by two Cologne brothers, both in their early 20s, while they were doing repair work in the basement of their parents' house in order to strengthen its foundations. They hadn't dug more than a few inches when their spade tips struck a limestone block carved with the figure of Pan. The amateur archeologists-by-accident recruited some friends and during the next five years put in 13,000 hours of hard work to clear and lift the huge, perfectly preserved structure out of their family's house on Chlodwig Square. They sold it to the museum, whose centerpiece it is today.

One could spend days in this museum. The collection of art and craft objects provides a singular insight into everyday Roman and early Frankish-German life. The intricately worked glassware items, from workshops that started in Cologne around A.D. 50, are among the finest in the world.

From the Roman-Germanic it is but a few steps, albeit nearly a 2,000-year leap, to the Ludwig Museum and its stunning collection of modern art. Nearly every object in it is a gift from Peter Ludwig, 60, an art historian by training, a chocolates and candy manufacturer by profession. In more than 30 years of judicious buying and bidding, he has amassed nearly 4,000 art treasures, spanning three millenia of human creativity, conservatively valued at $300 million. They are on permanent loan and donations to 21 major European museums, three of which, including the one in Cologne, bear his name.

The contemporary American section -- Warhol, Lichtenstein, Rauschenberg, Johns, Oldenburg, Estes, Segal, Hanson, to name but a few of the artists represented almost wholesale -- is so huge and comprehensive that U.S. museums must draw on the Ludwig hoard in order to stage retrospective exhibitions.

Cologne may stand for carnival, churches, culture and commerce, but there is also a fifth "c" -- cuisine. It makes the city a dream for those who believe half the fun of traveling is eating and drinking.

Begin with the drinking. For all its association with the Rhine, the beverage of Cologne is beer, not wine -- a unique beer brewed only in Cologne, and believe it or not, the city has more breweries than Munich. It is called Ko lsch. The capital "K" is vital, making it a noun. The same word, written small, is the adjectival form of Ko ln in local dialect, which is unpronouncable for outsiders until they've had a few Ko lschs too many.

A light, top-fermented beer of 3 percent alcohol content, it must be served in a distinctive half-pint glass, 2 inches in diameter, 7 inches tall, which is called a stange, a rod. It is sold only on tap in typical Ko lsch pubs and taverns, of which there are hundreds, including several with centuries-old pedigrees and their own breweries. The waiter who serves it is called a Ko bes and wears a dark-blue knitted vest and a dark-blue ankle-length linen apron. The proper snacks to eat with it are such rustic things as ko lsch Kaviar, Cologne caviar, meaning blood sausage and onion rings, or halve Hahn, which translates as "half a rooster" but is actually a thick slab of Dutch cheese on half a hard roll. Ko lsch also is used to wash down such local specialties as sauerbraten and potato pancakes.

Of course, there is also plenty of wine, above all from the Rhine, the Moselle and the Saar, and no dearth of wine taverns and restaurants. Prodigious tippling has a 2,000-year tradition, after all. Indeed, among the more amusing objects in the Roman-Germanic museum are wine glasses, goblets and tankards with such Latin inscriptions as Ergo Bibamus, Da Merum and Prosit, meaning roughly: "Let's drink," "Pour it straight" and "To your health."

The culinary palette is immense, ranging from simple, hearty German food to sublime Michelin-starred cuisine. In fact, among Germany's largest cities, only Munich has more top-rated restaurants than Cologne. Among the best of them are the Michelin three-star Goldener Pflug in the suburb of Merheim, where reservations three weeks in advance may be necessary, and Roland Bado's exquisite La Poe le d'Or on Komo dien Strasse, both ranked among the 10 top restaurants in the country in every guide.

On an almost equal plane are the one-star Chez Alex on Mu hlen Gasse, Franz Keller's Restaurant on Aachener Strasse and Auberge de la Charrue d'Or on Habsburger Ring. These are French in their approach, and both Roland Bado and Franz Keller are masters of nouvelle cuisine. Bei Rino on Ebert Platz is the only Italian restaurant in Germany that has a Michelin star.

While the idea of eating French or Italian cuisine in Germany may seem a bit abstruse in other cities, Cologne is a justified exception. After all, Italians, who are now back in force with more than 50,000 of them living and working in the city, founded it, and the French, don't forget, owned and ruled it for three decades.

Besides, from the day of its founding 20 centuries ago, scheming Agrippina's "Colonia" was a cross-cultural melting pot and a crossroads of the known world. It still is.