1. Definitions and examples2. Maps and relations on sets3. Elementary consequences of the definitions4. Subgroups5. Cosets and Lagrange's Theorem6. Error-correcting codes7. Normal subgroups and quotient groups8.

The Homomorphism Theorem9. Permutations10. The Orbit-Stabilizer Theorem11. The Sylow Theorems12. Applications of Sylow Theorems13. Direct products14. The classification of finite abelian groups15. The Jordan-H"older Theorem16.

Composition factors and chief factors17. Soluble groups18. Examples of soluble groups19. Semi-direct products and wreath products20. Extensions21. Central and cyclic extensions22. Groups with at most 31 elements23. The projective special linear groups24.

The Mathieu groups25. The classification of finite simple groupsAppendix A Prerequisites from Number Theory and Linear AlgebraAppendix B Groups of order 32Appendix C Solutions to ExercisesBibliographyIndex.