See also: Symmetry for the visual geometric symmetries that motivated the abstraction, Representation Theory for groups acting on vector spaces, and Lie Groups for the continuous version where group elements form a manifold.
The visual entry point -- discover groups through the symmetries of polygons
Formalize the four axioms visually using symmetry shapes
Build stunning diagrams that reveal a group's entire structure at a glance
Color-coded Cayley tables that expose patterns, symmetry, and subgroup structure
Stunning Cayley tables from Q8, all order-8 groups, and larger groups like A4 and D5
Find substructures within groups and partition elements into equal-size cosets
Build new groups from old ones and watch quotient groups collapse into existence
Structure-preserving maps between groups -- kernels, images, and isomorphisms
A visual atlas of all groups up to order 8 with their diagrams and properties
The power of prime-power-order subgroups -- existence, counting, and conjugacy