This volume, an introduction to the theory of modules. After developing the basic notions in modules and vector spaces with applications to ranks and linear equations, diagonalizable and triangulizable matrices (with special results on real and complex matrices), modules over principal ideal domains and canonical forms of matrices under similarity reduction. The authors give an exposition of the general theory of quadratic forms and the Hasse-Minkowski theory of rational quadratic forms, projective and injective modules, tensor products and flat modules. The abundance of interesting exercises in each chapter would strengthen the reader's grasp of the subject matter and widen his perspective. " - emphasis on carefully selected exercises is one of the outstanding features of the present book, apart from the adept arrangement of the material, its utmost lucid and detailed representation, and its remarkable versality. No doubt, this is one of the very best introductions to basic module theory at all."