Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are easily accessible to non-experts and undergraduates alike. The author deals with many different approaches to the study of squares; from the classical works of the late 19th century, to areas of current research. Anyone with an interest in algebra or number theory will find this a most fascinating volume.

"A well-written, unpretentious introduction to squares and sums of squares in fields." American Mathematical Monthly

"...Rajwade's exposition...is richly detailed: the reader is not forced to reproduce complicated algebraic calculations just to follow the arguments. Even more delightful is how Rajwade approaches the frontiers of current research in certain aspects of the algebraic theory of quadratic forms without significantly increasing demands on the reader! Highly recommended." D.V. Feldman, Choice

"Anyone wanting to learn something about the algebraic theory of quadratic forms will find this book useful. It is written at an elementary level, accessible to undergraduate students. At the same time, it contains several important topics, including the classical theorems of Hilbert, Hurwitz and Radon, not covered in the standard references." Murray Marshall, Mathematical Reviews

"...this book includes beautiful and important mathematics which can be explained at a fairly elementary level. Many of these theorems have appeared only in research journals and certainly deserve to be advertised in expository books and appreciated by a wide audience." Daniel B. Shapiro, The American Mathematical Monthly