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I want to study algebraic topology on my own. I just finished a semester of pointset topology and three weeks of algebraic topology. We did not use a textbook. Can anyone recommend a book on algebraic topology?

Hatcher is fine but it is not as rigorous as I want. Munkres has a book on algebraic topology but it is kind of out of date. If no one has a better suggestion then I will probably switch between Hatcher and May. But I want to try my luck here first. Thanks!