One of the standbys of the old "Ripley's Believe It or Not!" cartoon went something like: "The City of London, The capital of Englnd, is just one mile square!What's more, it has a population of less than 5,000 Believe It or Not!"

Well, you can believe it. The City of London, population 5,000 and modest in its dimensions, is not to be confused with the rather grander but implacably lower-case city of London, population 8 million. The City -- or the Square Mile, as it is more affectionately known -- is the historical, if not quite geographical, heart of Britain's capital. It is a dense and bewildering -- and curiously little-known -- tangle of crooked lanes and shadowy passageways, where great institutional buildings hunch together like oversized books on a crowded shelf. This is where London's history was made: where the Great Fire raged, where London Bridge fell down, where Pepys lived and Dickens drank and Shakespeare came of age.

Originally what we now think of as London was two distinct places: the City of London and, about two miles upriver, the City of Westminster. All the other parts of modern London -- Chelsea, Fulham, Hampstead and so on -- were scattered villages.

Today the City remains very much a place apart, an independent community with its own laws and law courts, its own police force and its own distinctive street signs; a place with a fiercely cherished right of independence enshrined in the Magna Carta, where even the queen cannot officially venture without permission. Believe it or not.

The City contains, among much else, St. Paul's Cathedral, the Bank of England, Lloyd's of London, the Royal Exchange, Baltic Exchange (for shipping) and Stock Exchange, the Central Criminal Court (universally known as the Old Bailey), the Mansion House (home of the lord mayor), the College of Heralds, the Guildhall (the town hall), the Monument, the London Symphony Orchestra and Royal Shakespeare Company (both recently installed at the new Barbican complex), the much overlooked Museum of London, a good many Roman ruins and the tallest building in the city (the National Westminster Bank tower). It also contains more than 40 churches -- a remarkable number for an area so small -- more than half of them by Christopher Wren.

All this history and bustling commerce are packed into just 677 acres -- an area not much larger than Regent's Park -- bounded on the south by the Thames and on the north by London Wall (along which ran part of the old Roman walls that once enclosed the City). Yet, apart from St. Paul's Cathedral at its western end and the Tower of London just outside its eastern boundary, the City remains oddly unknown to outsiders.

One reason is that it has never gone out of its way to attract them. The business of the City is business, and has been for more than 2,000 years. Despite the totterings of the British economy, the City is still the world's leading financial center. Its stock market is relatively small -- the total value of shares traded there is, at $290 billion, dwarfed by both Tokyo ($817 billion) and New York ($1.7 trillion) -- but even so the London Stock Exchange is the third largest in the world and many times larger than all the other European stock markets combined.

But it is in international business that London is truly supreme. The City is the world hub of such arcane financial instruments as Eurobonds, floating rate notes, traded options and financial futures. These markets are often as vast as they are mysterious. The London Eurobond market, for instance, has deposits of $2.5 trillion, making it a good deal larger than both the New York and Tokyo stock markets.

The City is also the world center for shipping, insurance, reinsurance, foreign exchange (with daily turnover a whopping $150 billion) and most of the main commodities. The price of the coffee you drink, the chocolate you eat, the gold in your teeth is largely decided here. If you own a diamond, chances are it has been weighed and parceled in an anonymous-looking building off Holborn Circus, the headquarters of De Beers, the international mining company. So central is the City to the world's economy, in fact, that there are now more American banks with branches in London than in New York.

Like most ancient things, the City of London has taken some knocks in its time. It was devastated first by the Great Fire of 1666, which destroyed 13,000 houses and reduced to ash virtually the whole of the medieval city, and then by German planes in 1940, which leveled much of it once more.

Today what remains is largely a Victorian district superimposed onto a medieval street plan, where stolid edifices of Portland stone and marble stand grandly alongside absurdly narrow streets. About all that remains of the ancient City of London are a few lengths of Roman wall, which often crop up unexpectedly -- one section is preserved along Platform 1 of the Tower Hill Underground station -- and some unfailingly curious and intriguing street names: Garlick Hill, Crutched Friars, Threadneedle Street, Bleeding Heart Yard, Pope's Head Alley, Seething Lane, Addle Hill.

No less remarkable are the names of the City's churches: St. Andrew Undershaft, All Hallows Barking, St. Sepulchre Without Newgate, St. Giles Cripplegate (where Oliver Cromwell was married and John Milton is buried) and the truly unbeatable St. Andrew-by-the-Wardrobe. But those are just their everyday names: Often the full, official titles are even more breathtaking, as with The Lord Mayor's Parish Church of St. Stephen Walbrook and St. Swithin Londonstone, St. Benet Sheerhogg and St. Mary Bothall With St. Laurence Pountney (which is, for all that, just one church -- by Wren, of course -- and an exceptionally pretty one at that). Also notable is St. Mary-le-Bow, on the street called Cheapside, which contains the famous Bow Bells, within whose sound you must be born to be a cockney.

The compactness of the City has always been one of its greatest virtues, and almost all that the international executive could need -- or the tourist wish to see -- is within walking distance of Bank (never the Bank, but just Bank), the epicenter of the City, where nine streets converge and around which stand the Bank of England, the Royal Exchange (built by Sir Thomas Gresham and now home of the London International Financial Futures Exchange) and the Mansion House, the 18th-century residence of the lord mayor.

Despite the grandeur of the buildings hereabouts, it is worth remembering that most of the City's exchanges started quite informally in coffeehouses -- which explains, for one thing, why the red-coated messengers at Lloyd's, the insurance market, are still called waiters. (Traditions tend to linger in this part of the world.)

Cornhill, the City's handsomest thoroughfare, runs east from Bank to Leadenhall Market, a colorful, vaulted-ceiling assemblage of shops, most of them given over to selling food. Beyond that soars the extraordinary and controversial new headquarters of Lloyd's, a vast space station of gleaming aluminum and external pipe work. It is well worth a look. But you may never get that far, so seductive are the little side lanes and courtyards that lie off Cornhill, beckoning with glimpses of cramped churchyards and smoky pubs and the aroma of half-hidden restaurants. To venture into these shadowy lanes is to step into the London of Dickens and Sherlock Holmes and Jack the Ripper.

Into the City's cramped streets each weekday pour more than half a million workers. From 9 to 5 the sidewalks are crowded with gravely busy men in pin-striped suits, and every narrow street becomes a frozen river of cars and trucks and delivery vans (which sit motionless for vast periods and then surge into life just as you step off the curb).

In an area where even the main thoroughfares are so narrow that trucks sometimes bump up onto the sidewalk -- a distinctly unnerving experience to anyone with feet in the vicinity -- and where the layout of the roads has all the orderliness of a bowl of spaghetti, anyone unfamiliar with the territory may be forgiven for quickly retiring exhausted.

But in the evenings and on weekends, when the bowler-hatted bankers and brokers flee to suburban comforts, the City grows eerily empty, its cavernous byways preternaturally quiet, the only sounds the rustle of dried litter in the gutters and the remote hum of distant traffic. You can stand outside the ghostly banks and almost hear the interest accruing.

That is the time to come to the City. The famous buildings will all be shut, of course, but few of them open their doors to tourists anyway. The Stock Exchange, which has a visitor's gallery, is one noble exception, but on the whole the City has a lot to learn about public relations. There are, in any case, only two conventional tourist attractions in the City, and happily both are open on weekends.

The first is the Monument (at the junction of Monument Street and Fish Street Hill), a sturdy, 202-foot-high column built by Christopher Wren as a memorial to the Great Fire of 1666. Its height corresponds exactly to the number of feet from it to the bakery shop in Pudding Lane where the Great Fire started. You can climb a spiral staircase to the top for 50 pence. It is a long, long trudge up 311 well-worn steps (just when you think you must nearly be there you come across a sign that says "Halfway"), but the view at the top -- a panorama across the whole of London -- is easily worth the risk of a pulled hamstring.

The other compulsory attraction is the Museum of London, at the Barbican complex, just north of St. Paul's. Like the Monument, it is a great favorite with British schoolchildren and, apart from a few harassed-looking teachers, you could find yourself the only adult there. But the displays are excellent and imaginative, and nowhere else can you get such a quick idea of just how thickly layered in history London is. Bill Bryson lives in London, where he works for The Times.