In this part, we dive deeper into the theory of groups.

Examples: 1

- Definition: Generating Set of a Group
- Definition: Group Homomorphism
- Proposition: Additive Subgroups of Integers
- Theorem: Construction of Groups from Commutative and Cancellative Semigroups
- Definition: Cyclic Group, Order of an Element
- Proposition: Finite Order of an Element Equals Order Of Generated Group
- Proposition: Group Homomorphisms with Cyclic Groups
- Lemma: Cyclic Groups are Abelian
- Lemma: Subgroups of Cyclic Groups
- Proposition: Subgroups of Finite Cyclic Groups
- Definition: Direct Product of Groups
- Definition: Conjugate Elements of a Group
- Definition: Cosets
- Proposition: Properties of Cosets
- Lemma: Subgroups and Their Cosets are Equipotent
- Theorem: Order of Subgroup Divides Order of Finite Group
- Theorem: Order of Cyclic Group (Fermat's Little Theorem)
- Chapter: Symmetry Groups
- Definition: Normal Subgroups
- Lemma: Factor Groups
- Lemma: Group Homomorphisms and Normal Subgroups
- Theorem: First Isomorphism Theorem for Groups
- Theorem: Classification of Cyclic Groups
- Theorem: Classification of Finite Groups with the Order of a Prime Number
- Definition: Group Operation