After making some historical remarks about the field, Nipp discusses grouping positive definite primitive quaternary quadratic forms into genera based on their large discriminants. He also includes Hasse symbols, the number of automorphs and the level of each such form, and the mass of each genus. The first 20 pages of the book are devoted to theory, and the remainder of the book contains a printed version of the tables based on large discriminants. A 3.5-inch disk formatted for a PC-compatible computer accompanies the book.

The book is suitable for advanced undergraduates with a strong background in linear algebra and computer programming, or for graduate students in the physical sciences or engineering who are looking for ideas for research. It is not appropriate as a student text, because most of the mathematical definitions and results used are merely stated, with a reference to the original source. The author’s approach of minimizing the mathematical explanations may not appeal to every reader. While the book will be difficult to use as a classroom text, it will be invaluable as a reference. Those topics that are not covered in detail are accompanied by complete references.

The author has done a good job of organizing a huge mass of data. The book is rigorous and will be a valuable asset for any researcher working in the area of quaternary quadratic forms.