TITLE: First book on algebraic topology
QUESTION [8 upvotes]: Is there a good book on introduction to Algebraic Topology which is self-contained and does not assume any background in topology, only standard calculus and linear algebra courses?

REPLY [2 votes]: The question about the first topology textbook has been asked and answered several times but what about specifically undergraduate textbook? Munkres has a good reputation but it's too dry in my opinion for a good undergraduate textbook. Kosniowski, mentioned above, is a very good choice with illustrations on almost every page. The only problem I have with it (and Munkres, and Basic Topology by Armstrong) is that its first topic in algebraic topology is the fundamental group. I prefer homology. The advantages are: (1) you can start with no point-set topology, (2) homology studies topological features of all dimensions instead of just one (cuts, tunnels, voids, etc.), and (3) you can connect homology back to calculus. For a short introduction to homology (with some point-set topology) I recommend  Topology of Surfaces by Kinsey and for a longer one my own Topology Illustrated.