Col. Weyand does for basketball, the most popular of all team games and the best attended of all sports, what he did for football in The Saga of Football (1955) and organizes its history competently for all followers. He establishes Naismith as its inventor, when, in 1861, a new gym game for fun and exercise was called for; he follows its rapid spread and the enthusiasm it aroused; he chronicles the changes in rules and other developments that came about through the years. His survey of college basketball is arranged by years (A.A.U. Championships, women's, international and pro basketball are covered in the same fashion) so that outstanding games, coaches, players and scores; the ever present questions of fouls; the shift in types of play -- from rough-house to ""fire engine"" to ""race horse""; the scandals -- all have their place on the calendar. There's a short recap of the exploits of the Harlem Globe Trotters. With the Naismith Basketabll Hall of Fame to be opened in Springfield, Mass., next year, this should be an opening gun for that celebration.