This lively photographic guidebook takes readers into the fascinating history of  art patronage at the University of Illinois, from the first gallery's tentative beginnings in 1875 to collections now gracing campus museums and the everyday environment.   Placing her subjects in a social as well as art historical context, Muriel Scheinman provides engaging catalog entries that describe how various pieces came to the university and how critics, faculty, and students received them. She investigates the many works made for the Chicago medical campus by Works Progress Administration artists, reports on the influence of famous biennial exhibitions of contemporary American art mounted at the Krannert Art Museum, and relates stories of benefactor Robert Allerton's worldwide quest for art for his Monticello estate, which is now the university's educational conference center. Maps of the three locales enable visitors to find key murals, sculptures, and other objects presented in the text.   Laden with anecdotes about artists, donors, and works, A Guide to Art at the University of Illinois will surprise even art aficionados and diehard admirers of the University of Illinois.