Intended for an introductory-level class, this textbook outlines the preliminaries of abstract algebra and the algebraic extension fields before going on to discuss elementary group theory, polynomial equations not solvable by radicals, and finite groups. "Its pedagogical object is to introduce the fundamental structures of modern abstract algebra (fields, rings, and groups); its method is to set a problem as a goal and then to introduce the structures and their properties as they become necessary for the solution of the problem" (from the Preface). Redfield teaches at Hamilton College. Annotation c. Book News, Inc., Portland, OR (booknews.com)