This book has been designed to acquaint the students with advanced concepts of differential equations. Comprehensively written, it covers topics such as Boundary Value Problems and their Separation of Variables, Laplace Transforms with Applications, Fourier Transforms and their Applications, the Hankel Transform and its Applications and Calculus of Variations. While the textbook lucidly explains the theoretical concepts, it also presents the various methods and applications related to differential equations. Students of mathematics would find this book extremely useful as well as the aspirants of various competitive examinations.