Continue exploring homology in algebraic topology through a detailed examination of a simple graph-like space. Learn about cycles, boundaries, and homology as a quotient of cycles modulo boundaries, with separate groups for each dimension. Delve into commutative group theory, working with formal combinations of vertices, edges, and 2-cells organized into free abelian chain groups. Gain insights into the fundamental concepts of algebraic topology and their applications in analyzing topological spaces.