Say "Brooklyn" to the average American and it will trigger such associations as Ebbets Field, Coney Island, Brooklyn Bridge or the garbled diphthongs Hollywood invariably assigns to the GI from Flatbush. Say "Brooklyn" to a resident and the response is more apt to be the subway D train, Nathan's hot dogs, Junior's cheesecake and probably the name of a popular local saloon. Now try the same word on a former Brooklynite and you will hear, "It's not what it used to be." But, then, it never was.

While the fireworks, parades, commemorative medals and other hoopla attending the centennial of the Brooklyn Bridge tomorrow will focus attention on this most maligned of New York City's five boroughs, there is far more to the Brooklyn story, and McCullough has captured a lot of it in his sparklingly written, soundly researched account.

I approached this book with two assumptions. One was that its author was the David W. McCullough who wrote "The Great Bridge," that tingling tale of the construction of the 100-year-old span. The other was that, as one who grew up in Brooklyn, I knew practically everything there was to know about it. Wrong on both counts! The first error was dispelled in the book's foreword. David W. McCullough is not the same man as the historian David no-middle-initial McCullough; they are not even related. I discovered my second error before I was halfway through the book.

Brooklyn's early history was colorful. In 1609 Henry Hudson anchored the Half Moon off Coney Island before exploring the river that was to bear his name; by 1660 the Dutch West India Company had established six settlements in Brooklyn. The Dutch farmers grew tobacco and cotton, built stockades against marauding Indians and viewed with disapproval a seventh settlement, Gravesend, which was inhabited by British colonists and led by a woman. Lady Deborah Moody, says the author, was "probably the first woman, white woman at least, to be a political force in North America."

Among facets of Brooklyn history new to me was that in 1776 nearly one-third of its 3,700 inhabitants were black slaves. In the years before the Civil War, Brooklyn was anti-Abolitionist. It was a question of economics, not ethics. Almost half of its 267,000 citizens were immigrants who shared the fears voiced by the Rev. Henry Ward Beecher when he asked: "Are we ready to receive four millions of blacks . . . to compete with the present occupants of the labor market now overstocked?" Once war broke out, however, sentiment changed: 50,000 men turned out to answer Lincoln's call for volunteers in 1861, and Brooklyn women raised $400,000 for the medical services of the Sanitary Commission, forerunner of the Red Cross.

A substantial section of this book is devoted to the borough's extensive waterfront and its role as a major port. I found this informative but less entertaining than the chapter called "A City Having Fun" that deals, among other things, with the development of Coney Island. Sodom-by-the-Sea was what righteous Brooklyn burghers called it, and they were not far wrong.

"When Boss Tweed escaped from prison after his political empire fell apart, he hid out at a Coney Island bordello. When Carry Nation began to fall on hard times during her temperance campaign, she came to Coney, smashed up a few saloons and tobacco shops, and sold toy hatchets . . . to help make ends meet. After the gangster Legs Diamond was gunned down in Albany, his widow appeared at a Coney sideshow to lecture on the evils of crime. She did very well indeed and was saving up to open a gypsy tearoom when she made the mistake of saying there was more she would talk about. Two men, who left half-finished cigars behind on her kitchen table, dropped by one evening and shot her dead."

Equally diverting were the early days of the Brooklyn Dodgers. At the turn of the century, when the baseball team owned by Charlie Ebbets was in constant rivalry with the New York Giants managed by John J. McGraw, a characteristic encounter took place. "While McGraw was arguing with an umpire, Ebbets shouted something from his private box. McGraw shouted something back. 'Did you call me a bastard?' a furious Ebbets asked. 'No,' answered McGraw, 'I called you a miserable bastard.' " That, says the author, was the sort of thing Dodgers fans paid money to see and hear.

Always a collection of self-contained neighborhoods, Brooklyn today is even more markedly a borough of ethnic enclaves. There are separate communities of Poles, Italians, West Indians, blacks, Hasidic Jews, Scandinavians, Koreans, Haitians, Lebanese, Japanese and Chinese. The newest enclave is Brighton Beach, which Russian immigrants have turned into New Odessa.

Since World War II Brooklyn, like other urban areas, has seen decay, destruction and tremendous population shifts. The poorer sections on the perimeter, such as Brownsville and East New York, today bring to mind London after the blitz--blocks and blocks of demolished, burned-out, boarded-up houses. But there is also a strong move toward gentrification in areas closer to Manhattan where up-and-coming young couples have renovated solidly built 19th century brownstones.

Apart from the pleasures of its text and its 200 striking photographs, this book is a joy to read. Its oversized pages are of heavy matte stock whose wide margins and attractive layout are a credit to the publisher.