Reading list

There are quite a few books on algebraic topology that vary quite a
bit in terms of the level of the material and the topics that are
covered. Here is a list that very
roughly proceeds from more elementary to more sophisticated (but even
here you might perceive things differently).

Topology: James R. Munkres. The material on Algebraic Topology is only concerned with the fundamental group.

Basic Concepts of Algebraic Topology: Fred H. Croom. This book is probably closest to the contents and order of this class.

An Introduction to Algebraic Topology: Joseph J. Rotman.

Algebraic Topology: Allen Hatcher.