Logic and proofs
Set theory
Cartesian products, relations, maps and binary operations
The integers
Groups
Further properties of groups
The symmetric groups
Rings, integral domains and fields
Polynomial rings
Field extensions
Latin squares and magic squares
Group actions, the class equation, and the sylow theorems
Finitely generated abelian groups
Semigroups and automata
Isometries
Polya-burnside enumeration
Group codes.