1. Groups and homomorphisms
2. Vector spaces and linear transformations
3. Group representations
4. FG-modules
5. FG-submodules
6. Group algebras
7. FG-homomorphisms
8. Mashcke's theorem
9. Schur's lemma
10. Irreducible modules and the group algebra
11. More on the group algebra
12. Conjugacy classes
13. Characters
14. Inner products of characters
15. The number of irreducible characters
16. Character tables and orthogonality relations
17. Normal subgroups and lifted characters
18. Some elementary character tables
19. Tensor products
20. Restriction to a subgroup
21. Induced modules and characters
22. Algebraic integers
23. Real representations
24. Summary of properties of character tables
25. Characters of groups of order pq
26. Characters of some p-groups
27. Character table of the simple group of order 168
28. Character table of GL(2,q)
29. Permutations and characters
30. Applications to group theory
31. Burnside's theorem
32. An application of representation theory to molecular vibration.
