From the basic axioms to quotient groups, this chapter explores the fundamentals of Group Theory through beautiful problems and rigorous explanations.

This chapter covers:

- The group axioms and examples of groups
- Subgroups
- Abelian groups
- Homomorphisms
- Quotient groups

You'll build the same foundations as in a traditional Group Theory course, but you'll do it quicker, through more interesting problems, and with carefully crafted solutions and feedback on your answers. **Dive in!**