Patricia (Peaches) Freeman is a regular at the Capitol View Library in Southeast Washington, a two-story, tan brick structure whose vitality and importance to its neighborhood have survived budget cuts, vandalism, theft, staff reductions and all the other insults of a telecommunications age.

Freeman, a jovial 22-year-old, went to the library almost every week for books on child care when she was expecting her first baby. Now she comes in--with baby--to catch a free film or swap baby stories with the librarians, who are mothers, too.

Substitute teacher Lewis Burns is also a regular. He comes in every Monday to read the Sunday edition of The New York Times and scan the magazines his budget doesn't allow him to buy.

Catherine Allen is another well-known face. She just retired in November from the Treasury Department, and when it gets a little lonely at home she packs her thermos and comes by the library for a few hours, just "to be around people" and to read the Guide to the General Educational Development Test. Allen says she is brushing up so she can take a few courses at the University of the District of Columbia next semester.

Like Capitol View, each of Washington's 20 branch libraries has suffered problems--mostly big-city problems of more crime and less money--in recent years. Yet somehow the city's libraries survived, and they remain vibrant community institutions that offer much more than books and periodicals.

"I've always considered the library as more than a repository of books," said Hardy R. Franklin, the director of the D.C. library system, which is celebrating National Library Week. "We offer a variety of services to people, from the cradle to the grave."

People come to Capitol View, at the corner of 50th Street and Central Avenue SE, for Metrobus passes and tutoring, to get information on birth control, food stamps or help for an abused child, to take a "slimnastics" class, pick up income-tax forms, see a free film.

It's a place where teen-age boys scout out teen-age girls, senior citizens find a little company, young mothers get a bit of free baby-sitting for their children and outpatients from St. Elizabeths pass the time.

And yes, some people still come in to read and take out books. Although the number of people who walked into the city's libraries decreased last year, the number of books and other materials circulated increased by 61,597 to more than 1.5 million.

The library, sandwiched between St. Luke's Catholic Church and low-income housing on one side, and the Leading Commandment Church and substantial red-brick single-family homes on the other, has special meaning for the Capitol View residents. They fought to get it built.

No one heeded their pleas for a community library until 10-year-old Francel Trotter, wearing her best Sunday dress, brought their case to the Senate subcommittee on District appropriations in 1961 and won the help of Sen. Harry Byrd.

Trotter is now 30 and a lawyer in New York. A plaque with her picture and the newspaper clipping on her testimony that day in Congress hangs on the library wall. Her mother is still a regular library patron.

"It's been a long pull to get things like a good bus route, decent roads and the library," said Adelaide V. Barnes, who's lived in the Capitol View area since 1940.

Barnes is a retired nurse and president of the Friends of Capitol View Library. Their credo is, "We believe the library is the cultural center in a community." That is also why the Capitol View residents--many of whom are current or retired government workers--cringe at steady, but so far unsubstantiated, rumors that their branch library may close for lack of use.

"Everytime we look around, there's something being taken away from us," said Dorothy Koger, a retired survey statistician for the U.S. Census Bureau and a 40-year resident of the community. Koger was at the library one day last week, checking out "The Life of Saint Paul."

Capitol View has never had a major supermarket chain or drugstore in that area. A number of small, black-owned businesses have been sold to immigrants recently, the residents said.

"We shouldn't have to defend the library. It should be one of the last things on the list to be closed when we need learning so badly, especially in the black community," said Arthur Darby, 51, another Capitol View resident who remembers coming to the library to copy information from medical books for his wife when she was in nursing school 20 years ago. He still comes in after work to read books like "Let Go and Let God."

"As long as one child comes through that door, this library is worth it," said community activist Vera Thompson. Thompson said she has visited Lorton reformatory and found not only that many of the inmates have reading problems, but that a number of them had lived in Ward 7, where Capitol View is located.

Book circulation at Capitol View declined slightly last year. So did the number of people using the library. But the branch ranked second in the city in use for community meetings.

About 300 to 400 books in the library's 28,000-book collection are not returned each year, said chief librarian Norberta Claiborne. Electric scanners have now been installed at the library's exit and the names of people who do not return books are recorded in a computer file.

Break-ins occur periodically and the coins from the copying machine are stolen. Vandals have scrawled graffiti on the library's exterior walls, but Capitol View has otherwise escaped serious vandalism, Claiborne said.

Many of the people who use the branch have a personal story to tell about themselves and their library. It was at Capitol View that 21-year-old Ifa Shango, an urban studies student at Prince George's Community College, picked up a book called "How Men Worship." The book, he said, spurred him to do further research on world religions, which changed his whole outlook on life.

Jeanette Garcia, who lives just across the District line in Prince George's, says her weekly outings to the library with her two children, Maya, 4, and Christopher, 2 1/2, has brought them closer together.

"Sometimes you get so fixed on taking care of their physical needs, or telling them, 'Don't do this, don't do that,' that you forget how interesting your children can be," Garcia said.

Claiborne said she and her staff have tried to make people at home at the library. "As a kid, I never felt welcome at the library. It was a place where you got shushed." Claiborne says many of the teen-agers who come in after school to do their homework wind up talking to the staff about their personal problems.

"Libraries have changed. They're a lot noisier than they used to be," Claiborne said. "But my philosophy is, this is a community place."