Understanding groups

            1. Understanding groups
            2. Multiplying subsets
            3. A different way of defining subgroups
            4. The modular law
            5. Multiplying cosets

Automorphisms

            1. Automorphisms
            2. Examples of automorphisms
            3. The automorphism group
            4. Automorphisms in modular arithmetic

Conjugation

            1. Conjugation
            2. Conjugacy classes
            3. Conjugation in permutation groups
            4. The centralizer
            5. The size of a conjugacy class
            6. Inner automorphisms

Normal subgroups

            1. Centralizers and normalizers
            2. Normal subgroups
            3. The coset property of normal subgroups
            4. The quotient group
            5. Normal subgroups of normal subgroups

Homomorphisms

            1. Homomorphisms
            2. Many-one homomorphisms
            3. The kernel of a homomorphism
            4. The image subgroup

The isomorphism theorems

            1. The first isomorphism theorem
            2. An example
            3. Proof of the theorem
            4. The second isomorphism theorem
            5. Proof of the theorem
            6. The third isomorphism theorem
            7. The Zassenhaus Lemma
            8. Composition series
            9. The Jordan-Hölder Theorem

Group actions

            1. Left and right actions
            2. Orbits
            3. Stabilizer subgroups
            4. Free actions and effective actions
            5. Actions and permutation groups
            6. Self-actions and Cayley's Theorem
            7. The orbit-stabilizer theorem

New groups from old

            1. Direct products
            2. Direct sums of abelian groups
            3. Finitely-generated abelian groups
            4. Proof of the theorem (part 1)
            5. Proof of the theorem (part 2)
            6. Proof of the theorem (part 3)
            7. Proof of the theorem (part 4)
            8. Semi-direct products

Sylow's Theorem

            1. The need for Sylow's Theorem
            2. Proof of part 1
            3. Proof of part 2
            4. Proof of part 3

Matrix groups

            1. Families of matrix groups
            2. Affine groups
            3. Complex matrix groups
            4. Linear representations
            5. Schur's Lemma