

An algebraic structure is a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. Examples of algebraic structures include groups, rings, fields, and lattices.

• ## 1: Symmetry

Groups arise in nature whenever we can find symmetry. For example, the human body has a lateral symmetry: if you imagine reversing left and right, most people would look more-or-less the same.

• ## 6: Group Actions

In this chapter, we examine group actions and some fun applications of group theory.