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Much clearer than any other topology books I've seen with the possible exception of Michael Henle's "Combinatorial Topology".I really like the style and in fact the entire "Springer Undergraduate Mathematics Series".It's about as gentle as you could find with all the things you could typically want, plenty of examples, explanations and exercises with a clear emphasis on key concepts and lots of motivation.Now this came out a while ago so perhaps there is something newer and better, but on the ot...
This excellent book is divided into two main parts. The first part develops general notions in point-set topology, particularly the ones that will be needed in the second part. The second part is about algebraic topology, of which three main areas are explored: homotopy, simplicial homology (divided into the homology of non-oriented simplices and of oriented simplices), and singular homology. Crossley has an excellent way of explaining concepts in this fascinating but often difficult subject, us...