Compelling spring reading; First span over East River The Great Bridge: The Epic Story of the Building of Brooklyn Bridge, by David McCullough. New York: Touchstone Books. 636 pp. $9.95.

How many people are interested in reading the story, in 634 pages, of the building of a bridge? If it is this book, the answer is ''lots of people.'' ''The Great Bridge'' is a phenomenal achievement, treating the Brooklyn Bridge from its conception to its opening, and beyond. The Roeblings, who carried out the construction, Boss Tweed, Henry Ward Beecher, and a host of other characters appear throughout this engrossing story.

McCullough frequently digresses fr/m the main story, and yet he never trivializes. His keen sense of the drama of history enables him to bring to life the secrets it holds.