CONTENTS; PREFACE; 1. GROUPS; 1.1. MONOIDS; 1.2. THE BASIC IDEA OF A GROUP; 1.3. CONTINUOUS GROUPS; 1.4. GROUP OPERATIONS ON A SET; 1.5. NORMAL SUBGROUPS; 2. VECTOR SPACES; 2.1. BASIC DEFINITIONS; 2.2. NORMED VECTOR SPACES; 2.3. SCALAR PRODUCTS; 2.4. LINEAR OPERATORS; 2.5. UNITARY OPERATORS; 2.6. THE USE OF UNITARY OPERATORS IN QUANTUM THEORY; Rule 1; Rule 2; 3. GROUP REPRESENTATIONS; 3.1. BASIC DEFINITIONS; 3.2. SYMMETRY TRANSFORMATIONS IN QUANTUM THEORY; 3.3. REDUCIBILITY OF REPRESENTATIONS; 3.4. IRREDUCIBLE REPRESENTATIONS; 3.5. GROUP CHARACTERS; 3.6. THE GROUP ALGEBRA; PROBLEMS; SOLUTIONS
