This book has been written strictly according to new curriculum for Second Year: Second Semester students at all Universities of Andhra Pradesh. It covers important topics such as Vector Spaces, Basis and Dimension, Linear Transformation, Fundamentals of Matrices, Characteristic Values and Characteristic Vectors, Cayley-Hamilton Theorem, Inner Product Spaces, and Orthogonality. The book will guide the students in a proper way and inspire them to sure and brilliant success. The authors are very happy that the earlier editions have been very well used by the students.