This is a table of contents for my notes on Group theory. The posts are arranged in an order that might be found in a textbook. For an alphabetical index, see this page.

- Definition of a group
- Subgroups and Lagrange's theorem
- Group multiplication tables and order-6 groups
- Direct products of groups
- Permutation groups - cycles and transpositions
- Cayley's theorem
- Equivalence classes
- Cycle structure of permutation groups and partition of integers
- Equivalence (conjugacy) classes of permutation groups
- Dihedral groups
- Equivalence (conjugacy) classes of dihedral groups
- Quaternions as groups
- Quaternion arithmetic
- Vectors as quaternions
- Exponential of a quaternion
- Rotations using quaternions
- Rotations in general using quaternions
- Coxeter groups
- Invariant subgroups
- Derived subgroups
- Cosets and quotient groups
- Sets, groups, fields, vector spaces and algebras

- Lie groups, Lie algebras and rotations
- Lie algebra of the rotation group SO(n)
- Representation of rotation group with rank-2 tensors
- Irreducible representations of rotation group
- Invariant symbols and dual tensors

- Representations and characters of groups
- Regular representations of groups
- Unitarity theorem for groups
- Two-dimensional representations of the permutation group
- Schur's lemma
- Great orthogonality theorem
- Character orthogonality
- Sizes of irreducible representations
- Class algebra
- Character table for S₄
- Character table for S₄ using the regular representation
- Real, pseudoreal and complex representations
- Test for real, pseudoreal and complex representations
- Square roots of group elements