This book is a compilation of all basic topics on functions of several variables and is primarily meant for undergraduate and post graduate students of all Indian universities. The salient features of the book are: , 1 This book includes a rich collection of problems and solutions which illustrates well known fundamental theorems. their proofs and necessary concepts. In each chapter, the basic concept of the concerned topic is discussed in a simple and lucid manner. Large number of problems have been suitably framed, properly graded and are given in right places. Topics covered are limits, continuities and differentiabilities of functions of several variables; properties of Implicit functions and Jacobians; extreme values of multivariate functions; various types of integrals in planes and surfaces and their related theorems including Dirichlet and Liouville's extension to Dirichlet.