This monograph is a thorough introduction to the AtiyahSinger index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory. The book is designed for a complete proof of the \(K\)theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, RiemannRochHirzebruch theorem, and the AtiyahSegalSinger fixed point theorem, etc. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership Graduate students and research mathematicians interested in \(K\)theoretic index theorem. Table of Contents  \(K\)theory
 Fredholm operators and AtiyahJädnich theorem
 Bott periodicity and Thom isomorphism
 Pseudodifferential operators
 Characteristic classes and ChernWeil construction
 Spin structure and Dirac operator
 Equivariant \(K\)theory
 The index theorem
 Cohomological formulation of the index theorem
 Bibliography
 Index
