Geometric Simplicial Complexes - Related Books

Mathematics++: Selected Topics Beyond the Basic Courses (Student Mathematical Library) Kantor, Ida.

Chapters:

1. Measure
2. High Dimensional Geometry
3. Fourier Analysis
4. Representations of Finite Groups
5. Polynomials
6. Topology

Chapter 6 - Topology. Contains a relatively gentle introduction to homology.

Graphs, Surfaces and Homology - Peter Giblin.
Builds up to homology groups via graphs and simplicial complexes.