Correction Appended

THE breeze off New York Bay blows gently over scenes of the new and the old in the Bay Ridge section of Brooklyn. In Dyker Beach Park, a group of elderly Italian men play boccie on a Sunday afternoon. Blocks away, Asian immigrants, newcomers to Bay Ridge, window-shop along 86th Street.

On the bluff overlooking the bay, a developer demolished Hamilton House, a popular neighborhood restaurant, to build an apartment complex. But there is a new restaurant in the Hamilton House complex, and it has kept the old name, just as the community has retained many of its old traditions.

This neighborhood on the southwestern bulge of Brooklyn has been known for its stability and small-town atmosphere since Norwegian ship carpenters settled there in the late 1800's. The Dutch, another seafaring people who arrived in 1653, were the first to arrive.

In the last decade, new ethnic groups have joined a community once dominated by the Irish, Scandinavians and Italians. Longtime residents say all newcomers are welcome.

The ethnic diversity of the community is reflected in the proliferation of restaurants that have sprouted along Third Avenue.

Steaks and other American specialties are popular at Embers, a new restaurant run by two Italian families, the Malafronts and the Rocanellis, who have operated Vinnie's Meat Market nearby for 30 years. There is Indian cuisine at India Passage, tempura at Fujisan and stuffed artichoke and fettuccine Alfredo at Canedo's.

Third Avenue, Fifth Avenue and 86th Street are the liveliest shopping lanes. New boutiques and bars alternate with established food shops and dusty hardware stores. On Third Avenue near 76th Street, Pat Conaghan manages Classy Coffees, a sweet-smelling cafe that opened last year, selling coffees, coffee beans and desserts.

''Third Avenue was going down and now it's picked up,'' said Mrs. Conaghan. On Saturday nights, many of Bay Ridge's residents dine on Third Avenue and then go to one of the cafes for dessert, she said.

The community's homes are as diverse as the people who live there. Detached brick homes with well-groomed lawns are common as are semidetached structures with a small front yard or a porch above the garage.

There are stone or stucco homes in the oldest sections of the neighborhood and it is not unusual to discover a Victorian with a wraparound porch tucked between a group of rowhouses.

Some of the most exclusive housing is found along Shore Road, a serpentine street with a view of New York Bay and the Verrazano-Narrows Bridge. In the last century, when this section of Brooklyn was primarily rural, Shore Road was dotted with large country homes. By the end of World War II, all but one of these mansions - Fontbonne Hall, now a Roman Catholic girls' school for grades 7 through 12 - had been torn down. In their place rose the many apartment buildings that provide most of the housing along Shore Road.

A two-bedroom cooperative in one of these renovated buildings sells for more than $200,000, said Frances Gaudio, who owns a real-estate company in Bay Ridge. A single-family house starts at $500,000 and can cost more than $1 million, said Georgia Costalas, who heads Shore Road Real Estate.

Shore Road has been the site of two of the largest housing construction projects in Bay Ridge in recent years. Four months ago the Seaside Development Corporation completed Hamilton House, on the site of the old restaurant of the same name.

Occupancy in the two-building project of 106 co-op apartments, with an equal number of parking spaces, is about 85 percent, said Michael Gherardi, a vice president at Seaside. Prices for the remaining studios and one- and two-bedroom apartments range from $70,000 to $212,000, Mr. Gherardi said.

Seaside also built the other project, the 210-unit Water's View at Verrazano, which was completed in 1982. All have been sold.

Another development with a view of the bridge was completed in June. The Harbour at Bay Ridge Condominium, with 52 one- and two-bedroom condominium apartments, has six two-bedroom condominiums left for sale, with prices ranging from $220,000 to $236,000, according to Henry Camuso, one of the developers.