The book is intended as a text for students of Physics at the Master's level. It is assumed that the students pursuing the course have some knowledge of differential equations and complex variables. In addition, a knowledge of Physics upto at least the BSc (Honours) level is assumed. Throughout the book the applications of the mathematical techniques developed to physics, are emphasized. Examples are, to a large extent, drawn from various branches of physics. The exercises provide further extensions to such applications and are often chosen to illustrate and supplement the material in the text. They thus form an essential part of the text. Readers are introduced to various common differential equations. Ordinary, second order and linear differential equations are discussed. Boundary value problems and special functions follow. Non-homogeneous boundary value problems using Green's functions are also developed. Other topics include linear vector spaces, group theory and tensors. Includes more than 100 solved examples, 160 exercises and 51 figures that emphasize physical problems to highlight application and reinforce learning.