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This textbook offers a primer in general topology (point-set topology), together with an introduction to algebraic topology. It's meant primarily for students with the mathematical background that's usually taught in the first year of undergraduate degrees in Mathematics and Physics. Around 500 exercises are included in the text: trying to solve them with dedication is the best way to attain a rm hold on the matter, adapt it to your own way of thinking and also learn to develop original ideas. Some exercises are solved directly in the text, either in full or almost.