Book Recommendations: Combinatorial Group Theory and Topological Prerequisites.
I assume you're familiar with the standard books in combinatorial group theory.
For combinatorial group theory and topology, try these books:
Classical Topology and Combinatorial Group Theory by John Stilwell
Combinatorial Group Theory: A Topological Approach by Daniel E. Cohen
Stilwell says in the preface:
The only prerequisites are some familiarity with elementary set theory, coordinate geometry and linear algebra, $\epsilon$-$\delta$ arguments as in rigorous calculus, and the group concept.
Cohen assumes familiarity with point-set topology.