The library contest that drew so many nominations was the idea of Reynold Levy, 71, a former president of Lincoln Center and a lifelong user of libraries.

At the time, budget cuts had forced many branches to eliminate weekend hours. Mr. Levy saw the contest as a way for people to show city leaders how much they valued libraries and to express their appreciation to those who work in them. The contest was sponsored by the Charles H. Revson Foundation and the Stavros Niarchos Foundation and awarded a total of $170,000 to 11 winning libraries, including $20,000 to the Inwood branch.

Mr. Levy, the chairman of Revson’s board of trustees, recalled that his first job, at age 14, was at the Brighton Beach library in Brooklyn, where he borrowed all his books. Four days a week, he would help check out books, collect fines and troll the aisles to make sure all the edges of the books were neatly lined up, climbing on stools to reach the upper shelves. “It was a dream of mine to be wealthy enough to build a library and buy books,” he said.

The recent gains by libraries have delighted Christian Zabriskie, a librarian and executive director of Urban Librarians Unite, an advocacy and education group that organizes an annual “read-in,” in which people take turns reading nonstop for 24 hours, to support the libraries.

“In New York City, there is somebody using library materials every second, every day of the year,” Mr. Zabriskie said. “It’s showing that libraries are the fabric of society.”