Keeping the modest goal as a text book on matrix theory the approach here is straight forward and quite elementary. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schur triangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least squares solutions_ It includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts; and problems have been added at the end of each chapter. Most of these problems are theoretical in nature and they do not fit into the running text linearly. Exercises and problems form an integral part of the book.