This part builds the language and the first definitions. By the end you can state the group axioms, verify them on standard examples, and recognise when two structures are “the same” up to relabelling.

Sequence

1. Introduction and Examples — sets equipped with operations; first examples and non-examples.
2. Binary Operations — closure, associativity, identity, inverses as standalone axioms.
3. Isomorphic Binary Structures — structure-preserving bijections and what they preserve.
4. Groups — the central definition and the abelian case.