Definition, morphisms, and basic groups

Identity, cancellation, equation and morphism properties

Subgroup, cyclic group, product group, intersection and join

Permutations

Transformation groups, representations, group action, automorphisms

Cosets

Kernel and image, center, automorphisms

Isomorphism theorems

Group extension

Characteristic subgroups

Conjugate classes

Sylow theorems

Nilpotent groups

Solvable groups

Jordan-Hölder theorem

Simplicity of alternating group