Preface -- Contents -- 1. REVIEW ON LINEAR ALGEBRAS -- 1.1 Eigenvalues and Eigenvectors of a Matrix -- 1.2 Some Special Matrices -- 1.3 Similarity Transformation -- 2. GROUP AND ITS SUBSETS -- 2.1 Definition of a Group -- 2.2 Subsets in a Group -- 2.3 Homomorphism of Groups -- 3. THEORY OF REPRESENTATIONS -- 3.1 Transformation Operators for a Scalar Function -- 3.2 Inequivalent and Irreducible Representations -- 3.3 Subduced and Induced Representations -- 3.4 The Clebsch-Gardan Coefficients -- 4. THREE-DIMENSIONAL ROTATION GROUP -- 4.1 SO(3) Group and Its Covering Group SU(2) -- 4.2 Inequivalent and Irreducible Representations -- 4.3 Lie Groups and Lie Theorems -- 4.4 Irreducible Tensor Operators -- 4.5 Unitary Representations with Infinite Dimensions -- 5. SYMMETRY OF CRYSTALS -- 5.1 Symmetric Operations and Space Groups -- 5.2 Symmetric Elements -- 5.3 International Notations for Space Groups -- 6. PERMUTATION GROUPS -- 6.1 Multiplication of Permutations -- 6.2 Young Patterns, Young Tableaux and Young Operators -- 6.3 Primitive Idempotents in the Group Algebra -- 6.4 Irreducible Representations and Characters -- 6.5 The Inner and Outer Products of Representations -- 7. LIE GROUPS AND LIE ALGEBRAS -- 7.1 Classification of Semisimple Lie Algebras -- 7.2 Irreducible Representations and the Chevalley Bases -- 7.3 Reduction of the Direct Product of Representations -- 8. UNITARY GROUPS -- 8.1 The SU(N) Group and Its Lie Algebra -- 8.2 Irreducible Tensor Representations of SU(N) -- 8.3 Orthonormal Bases for Irreducible Representations -- 8.4 Subduced Representations -- 8.5 Casimir Invariants of SU(N) -- 9. REAL ORTHOGONAL GROUPS -- 9.1 Tensor Representations of SO(N) -- 9.2 Spinor Representations of SO(N) -- 9.3 SO(4) Group and the Lorentz Group -- 10. THE SYMPLECTIC GROUPS -- 10.1 The Groups Sp(2l,R) and USp(2l).

10.2 Irreducible Representations of Sp(2l) -- Bibliography -- Index.