Basic but rigorous book for Abstract Algebra and Topology

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Could you recommend me a basic but rigorous book for Abstract Algebra and also another one for Topology? It'd be really great if it has a solution manual, or at least a great amount of solved problems. Thanks a lot.

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I personally really like the following book for learning abstract algebra: Contemporary Abstract Algebra by Joseph Gallian. It is a very good undergraduate level book for learning basics of algebra. It does have solution manuals available and also has answers for some of the questions in the back.