Representations and Characters of Groups

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.