Introduction to Topology (Dover Books on Mathematics)

This book is an excellent brief introduction to topology. Combined with a basic introduction to proofs and algebra, such as A book of Abstract Algebra by Pinter, this book allows anyone with a few calculus courses under their belt to learn the necessary topology to get into many other fields of mathematics, or to go deeper into topology. I've worked through both this and Munkres 2e, and I prefer Gamelin and Greene.

Good introduction to general topology

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Is a clear, elegant introduction: precise explanations, well-chosen examples, and a perfect balance between intuition and rigor. A great choice for students who want to truly understand topology without drowning in unnecessary technicalities.

Clear and concise with challenging exercises BUT answers to a majority of questions are in the back and are written out in full. A nice book for self-study and introduction to the field before taking a real course in topology.