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Topics from the theory of numbers (2nd edition), by Emil Grosswald. Pp 336. DM78. 1984. ISBN 3-7643-3044-9 (Birkhäuser)

The most accessible chapter for the general reader is probably the last one. This is an introduction to the theory of two-person games where each player has complete information and there are no chance moves. Although the relationship between these and theories of number is mentioned only briefly, the exposition is clear and newcomers will find it illuminating. Games with such wonderful names as Hackenbush, Maundy Cake, Rims and Rails, Cabbages and Brussels Sprouts are discussed and at least the reader will come across some interesting pastimes. Finally perennials such as Rubik's Cube, Sam Loyd's Fifteen Puzzle, Instant Insanity and Dots-and-Boxes are dealt with. The editors state in the preface that they have attempted to impose a uniform terminology and notation in the book and they are to be congratulated for their success in this respect. The high standard of presentation is remarkably homogeneous throughout.