• Elementary Topology: Second Edition by Michael C. Gemignani
  Superb introduction to rapidly expanding area of mathematical thought. Fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory and other essentials. Numerous exercises, plus section on paracompactness and complete regularity. References throughout. Includes 107 illustrations.
  Amazon.com: Elementary Topology: Second Edition (Dover Books on Mathematics) (9780486665221): Michael C. Gemignani: Books
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  Note: Recommended by John Banks.
• Introduction to General Topology by Joshi - amazon.com
  K. D. Joshi, Introduction to General Topology. A Halsted Press Book. John Wiley & Sons, Inc., New York, 1983. xii+412 pp. ISBN: 0-470-27556-1. K D Joshi obtained his Ph D in Mathematics from Indiana University,USA in 1972 and has been teaching mathematics at IIT Bombay since 1975. He has been involved with the conduct of the Joint Entrance Examination (JEE) in various capacities for over two decades. He has many books to his credit one of which is Calculus for Scientists and Engineers published by Narosa Publishing House in 2002.
  Amazon.com: Introduction to General Topology (9780852264447): K.D. Joshi: Books
  0852264445 2853116 and general introduction john joshi k.d ltd sons topology wiley
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  Note: Really good book. Lots of explaining of motivation, wordy in a good way. His personal homepage is found here: http://www.math.iitb.ac.in/~kdjoshi/ Melbourne Uni Maths library has a copy.
• Topology (2nd Edition) - by James Munkres - amazon.com
  This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
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  Note: John Banks recommended it. More formal than gemignani's 'elementary topology'.
• Topology Without Tears, chapters 1-10.
  "Topology Without Tears" by Sidney A. Morris. University of Ballarat, Victoria Australlia.
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• Beginning Topology (Brooks/Cole Series in Advanced Mathematics) by Sue Goodman
  With a nice balance of mathematical precision and accessibility, this text provides a broad introduction to the field of topology. Author Sue Goodman piques student curiosity and interest without losing necessary rigor so that they can appreciate the beauty and fun of mathematics. The text demonstrates that mathematics is an active and ever-changing field with many problems still unsolved, and students will see how the various areas of mathematics ? algebra, combinatorics, geometry, calculus, and differential equations ? interact with topology. Students learn some of the major ideas and results in the field, do explorations and fairly elementary proofs, and become aware of some recent questions.
  Amazon.com: Beginning Topology (Brooks/Cole Series in Advanced Mathematics) (9780534424268): Sue Goodman: Books
  0534424260 711014858-0534424260 advanced beginning brooks cole genera goodman mathematics science series sue textbooks topology
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  Note: A good broad introduction into some topological applications (a good 'overview' of what topology encompasses too); the four-colour problem, fixed-point theorems, fundamental theorem of algebra and knots. Glosses over point-set, seems to cover the important stuff. Her personal website can be found h ...moreere: http://www.math.unc.edu/Faculty/seg/ She recommends a history of Topology here: http://www-gap.dcs.st-and.ac.uk/~history/PrintHT/Topology_in_mathematics.html (I think Brian Davey also recommended this site)
• Elements of general topology by Donald Bushaw (2nd edition)
  Author: Bushaw, Donald. Title: Elements of general topology. Published: New York : J. Wiley, [1963].
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  Note: A really good, well worded account on point set topology, gives a good sketch of the motivation behind definitions. LTU Bundy's got it: https://alpha2.latrobe.edu.au/patroninfo/1119178/item&1287918
• Algebraic Topology by Allen Hatcher
  A bunch of books written by Allen Hatcher, in particular Algebraic Topology (described below) recommended by Grant... This is the first in a series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time. The first book contains the basic core material along with a number of optional topics of a relatively elementary nature. The other two books, which are largely independent of each other, are provisionally titled "Vector Bundles and K-Theory" and "Spectral Sequences in Algebraic Topology."
  A downloadable textbook in algebraic topology
  algebraic topology
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  Note: $30 off Amazon.com: http://www.amazon.com/Algebraic-Topology-Allen-Hatcher/dp/0521795400/ref=pd_bbs_sr_1/102-7670573-1396111?ie=UTF8&s=books&qid=1179353668&sr=8-1
• Open problems in topology edited by Jan van Mill, George M. Reed.
  Title: Open problems in topology / edited by Jan van Mill, George M. Reed. Published: Amsterdam [Netherlands] ; New York : North-Holland ; New York, N.Y., U.S.A : Distributors for the U.S. and Canada, Elsevier Science Pub. Co., 1990.
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  Note: Doesn't seem like they got to their third edition, despite saying it was due around 1995. Need to know a lot more topology before I can understand the problems.

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