Outline of the course

1. Definition of group, examples and basic properties.

2. Subgroups and generators of a group.

3. Cyclic Groups: definition, examples, their classification and main properties.

4. Morphism of groups and basic facts.

5. Symmetric groups, basic properties, and Caley´s Theorem.

6. Cosets, Lagrange´s theorem and consequences.

7. Normal subgroups and quotient groups.

8. Isomorphism and Correspondence Thorems.

9. Group action, basic facts, and Orbit-Stabilizer Theorem.

10. Class Equation and Burnside´s Lemma.

11. Sylow Theorem and its consequences.

12. Finitely Generated abelian groups.

13. Solvable groups.