For many people, "Rome" means ancient Rome, the world of the Caesars, Julius Caesar and Nero are etched in the memories of millions of once and present schoolchildren, and the "I, Claudius" of television and the "Caligula" of X-rated cinema keep the memory of ancient Rome fresh, if not pure.

For others, it is St. Peter's basilica and the Renaissance frescoes in the Vatican by Michelangelo and Raphael that define Rome. Still others, less historically conscious, may think of cafes on the Via Veneto or fashionable shops along the streets converging on the Spanish Steps.

But it is, in fact, another Rome -- that of the 17th-century baroque -- that binds al of the Romes together, that inifies the Rome of the Caesars, of the catacombs, of the Renaissance popes, and that largely dictated the Rome of today.

Dismiss the thought that baroque means excessively ornate or overly large. Instead, recognize baroque as the quintessential style of the 17th century -- with its dynamic curves and contrasts -- that embodies the optimistic, triumphant, celebratory spirit of the age.

Arguably the greatest achievements of the baroque in Rome are architectural, the construction of great palaces and churches and, above all, the formation of great public spaces. Often these spaces were pre-existing, but they had no order, no clear form or focus. It fell to the architects and sculptors of the 17th century, with Gianlorenzo Bernini preeminent among them, to impose or, as they would have understood it, to reveal the inherent order and power of the avenues and piazzas and marketplaces.

It is the element of surprise that is essential to the dramatic effect of these spatial creations. To a great extent the modern traveler still enters these piazzas from the density and relative confusion of the older, pre-baroque city. Stepping from the tangled network of medieval streets into the organized, theatrical grandeur of the baroque piazza is an astonishing physical and emotional experience with few parallels.

So, when in Rome, do as the travelers and piligrims of the 17th century did and go first to Piazza del Popolo, the northern gate through which most of them entered the Eternal City. Today, natives and visitors alike still gather on the terrace of the Pincian Hill as theyy have for centuries, to look down on the ageless piazza and across it to the west, as the sun sets behind the darkening dome of St. Peter's. It is, without doubt, one of the indelible sights of the world.

The Piazza del Popolo reached its present form over a span of 2,000 years, culminating in the elegant elliptical shape designed in the early 19th century by Guiseppe Valadier, architect to Napoleon. The great gate stands where te ancient gate stood at the beginning of the Flaminian Way, but in its present form it is the 16th-century work of Michelangelo.

Three great avenues fan out from the piazza, with two churches designed by Bernini (who was both an architect and a sculptor) between them, providing a dramatic stage set for the arriving visitor.

Pressed close to the gate is a third church, Santa Maria del Popolo, which legend holds to be built over the tomb of Nero. The foundations date to the 11th century, but as it stands, it is largely a Renaissance structure, with contributions by Raphael and Bramante, while Bernini restored and embellished the structure in the 1650s. The church holds a pair of great sculptures by Bernini in a chapel designed by Raphael and another pair of famous paintings by Caravaggio, the startling "Conversion of St. Paul" and "Crucifixion of St. Peter."

It was the visionary Pope Sixtus V who, between 1585 and 1590, gave shape and meaning to Rome, reviving its ancient quarters and aqueducts to bring the city to life under the "new Caesars," the popes of the 17th century; and it was he who began the practice of re-erecting the Egyptian obelisks taken as spoils by the ancient Romans. Here, in Piazza del Popolo, he ordered the architect/engineer Domenico Fontana to place the 13th-century B.C. obelisk brought to Rome under Augustus. Topped with a cross, it is the focal point, the keystone, to this triumphal gateway to the city. Sixtus' city plan established baroque Rome and dominates modern Rome.

Leaving the Piazza del Popolo, if you follow the Via del Babuino you will reach the Piazza Barberini, with its splendid baroque Triton Foundain by Bernini. To the right, on higher ground, is the Barberini palace, also the work of Bernini. Now a national museum, its chief masterpiece is the astounding painted ceiling of the great salon finished by Pietro da Cortona in 1639. Representing the glory of the Barberini family, whose head was then Pope Urban VIII, it swarms with allegorical figures including three gigantic bees, the busy clan's emblem. (It was the custom of the popes of the 17th century, all of whom were Italian, to spend considerable time "at home" in their family palaces. On such occasions the palaces. On such occasions the palace became the temporary center of papal authority.)

To the left is the beginning of the fashionable Via Veneto, whose sweeping curves were laid out in this century. With its exclusive hotels and social attractions it has come to symbolize the elegance of postwar Rome.

To a great extent, this is American Rome, with the palatial American Embassy standing near the beginning of the avenue. It is also the leisure-time soundstage for film stars and producers, and those who envy them.

But a short uphill walk form the Triton Fountain brings us back to baroque Rome with three significant monuments. First comes the so-called Moses Fountain, designed by Domenico Fontana, in which the Hebrw leader causes water to gush from the rock. It is at the end of an ancient aqueduct restored to use by Sixtus V. The pope's given name, Felice, gave the fountain its proper name -- Acqua Felice -- which also means "happy (or fortunate) water", which it surely was in a Rome then largely uninhabitable due to lack of water.

Two of the churches on the square embody the particular religious spirit of the 17th century. Santa Susanna is dedicated to an early Christian martyr, whose execution was believed to have occurred on this spot. Since the struggle of the early Christians against the Roman pagans was thought of as similar to the struggle of the 16th- and 17th-century Catholic church against the Protestant "heretics," the popularity of the early martyrs and the building of churches to honor them is readily understandable. The existing church of Santa Susanna was remodeled in 1603, at the outset of the baroque era, and the architect of its modest facade, Carlo Maderno, here prefigured the grandiose facade he would soon design for St. Peter's.

The paralle church of Santa Maria della Vittoria is famed for the elaborate, multimedia Cornaro or Saint Theresa Chapel, the epitome of Bernini's genius. Theresa was herself one of the most important reformers within the Catholic church of the 16th century, but in the 17th century the rapterous, mystical side of this extraordinary woman was even more significant. The vision she recounted of a beautiful angel who plunged an arrow into her entrails has sometimes bemused contemporary Freudians, but Bernini and many of his comtempories accepted the oneness of the mystical and the physical, of visionary and tangibile realities, and his levitating sculpture group continues to astonish all who see it.

This group of angel and saint is set above the altar in a stagelike projection flooded with seemingly miraculous light from a hidden window. The marble group has no visible support and seems suspended. On the side walls of the chapel Bernini has created, in high relief carving, members of the Cornaro family, which commissioned the chapel. Kneeling at prayer desks that look like theater boxes, they observe and discuss the apparition excitedly among themselves. High in the vault of the chapel, in a mixture of painting and carving, angels part the clouds to reveal the light of the Holy Spirit. The entire production is a calculated assault on the senses, designed to demonstrate spiritual love irresistibly. In calling on the full repertory of artistic materials and techniques for this purpose, the Cornaro chapel typified the Roman baroque at its most splendid.

If, upon leaving Piazza del Popolo, you follow the Via Ripetta, which runs nearer the Tiber, you will arrive at one of the most ancient areas of the city, centering on the Piazza Navona. While the whole neighborhood boasts famous baroque monuments -- such as the churches of Sant'Ivo, designed by Francesco Borromini, and Santa Maria della pace, by Pietro da Cortona -- no spot in Rome embraces more of the history of the Eternal City than this vast oval, some 780 feet long. In antiquity it was the Stadium of Domitian, whose form it retains and whose ruins it is built upon. During the long medieval centuries of Rome's decline, the city clustered chaotically around this core in the elbow of the river, but never intruded upon the open space, preferring to use it for markets and holiday celebrations.

Few buildings of any size were built here. But the Pamphili family had a palace on the piazza and, when Cardinal Pamphili became Pope Innocent X in 1644, the stage was set for the transformation of Piazza Navona into the wonder of Rome.

The Pamphili Palace was remodeled, the outstanding addition being a long gallery whose ceiling was frescoed by Pietro da Cortona with the history of Aeneas, form whom the family claimed descent. At the same time the church of Sant'Agnese was erected adjacent to the palace. Designed in the 1650s by the eccentric genius Borromini it was built, like Santa Susanna, on a spot associated with the early Christian martyr to whome it was dedicated. It was in essence a family church, wit a portion of the facade actually overlapping the palace at the spot where the pope's bedroom was, so that Innocent X repose, as it seemed, within the protection of the church. In fact, from this bedroom he could enter the church by a private staircase or even participate in the mass without leaving his chamber.

The ultimate dramatic stroke of baroque sculpture, Bernini's Fountain of the Rivers, is in front of Sant'Agnese. Initially out of favor with the Pamphjili, owing to his close association with the preceding papcay of the spendthrift Barberini family, Bernini had succeeded in reestablishing his artistic primacy in Rome. The great sculptor's theatrical bent was never better demonstrated than in 1651 on the occasion of the unveiling of this monumental fountain before the pope. Deeply impressed with the result of his patronage, Innocent X was only disappointed that the fountain was still dry. Bernini explained that the supplying aqueduct had not yet been connected, but as the potiff turned to leave, Bernini abruptly clapped his hans, and the fountain burst into watery life. A twice-enchanted pope returned happily to his palace.

The Fountain of the Rivers simulateously represented the continents then recognized (Europe, Asia, Africa, America) and the four rivers of Paradise (symbolic of the Gospels) dervied from the Book of Revelation. This particular blend of the secular and the sacred is the very essence of the 17th century. For Roman Catholism the expansion of the revitalized church went hand in hand with the unparalleled exploration of the globe.

Imagine, if you will, the layers of history and authority symbolically invoked on those occasions when Innocent X was "at home" in the Pamphili Palace and appeared at the window of the long gallery to bestow his blessing on the populace gathered in Piazza Navona. There he stood beneath the fresco of his ancestor, Aeneas, in the act of founding Rome. He looked out upon a public arena of great aniquity, now centered upon a heroic fountain symbolizing both the known world and the world hereafter. And he was flanked by the famiy church honoring a early mastyr. To Innocent X, at such a moment, Piazza Navona must have seemed the center of the world.

From the 17th until the mid-19th century, it was customery to flood the piazza on Sundays during July and August, the more spectacular equivalent of the opening of fire hydrants during our own urban heat waves. This offered as well the pretext for grand parties and processions among the elite.

There are no water festivals today, but Piazza Navona is still a festival stage on Jan. 5, when the eve of Epiphany ("Befana" in Roman dialect) is celebrated and the great space fills with the stalls of toy-sellers and crowds of horn-blowing, drum-punishing children. Italian children, in my experience, are expected to be heard as well as seen, and that is never more evident than during the exultant hours of Befana.

On any other day, as the modern visitor strolls in one of the most civilized public spaces to be found or savors a rich chocolate tartuffo at the Cafe Tre Scalini, this layered history is usually little known to him. But the great piazza, so casually enjoyed, is the reflection of the baroque era of Rome, one of the most dazzling legacies of European history.