Angular Momentum Techniques in Quantum Mechanics Angular Momentum Operators and Their Matrix Elements Coupling of Two Angular Momenta Vectors and Tensors in Spherical Basis Rotation Matrices I Rotation Matrices II Tensor Operators and Reduced Matrix Elements Coupling of Three Angular Momenta Coupling Of Four Angular Momenta Partial Waves and the Gradient Formula Identical Particles Density Matrix and Statistical Tensors Products of Angular Momentum Matrices and Their Traces The Helicity Formalism The Spin States of Dirac Particles. A course in angular momentum techniques is essential for quantitative study of problems in atomic physics molecular physics nuclear physics and solid state physics. This book has grown out of such a course given to the students of the M. Sc. and M. Phil. degree courses at the University of Madras. An elementary knowledge of quantum mechanics is an essential pre requisite to undertake this course but no knowledge of group theory is assumed on the part of the readers. Although the subject matter has group theoretic origin special efforts have been made to avoid the gro theoretical language but place emphasis on the algebraic formalism dev oped by Racah (1942a 1942b 1943 1951). How far I am successful in this project is left to the discerning reader to judge. After the publication of the two classic books one by Rose and the other by Edmonds on this subject in the year 1957 the application of angular momentum techniques to solve physical problems has become so common that it is found desirable to organize a separate course on this subject to the students of physics. It is to cater to the needs of such students and research workers that this book is written. A large number of questions and problems given at the end of each chapter will enable the reader to have a clearer understanding of the subject.