Reference request : Intro to geometry/topology for beginners I am looking for an introductory book in Topology, but one meant for a younger audience than is usually the case :
I am planning to do a reading course with some sophomore students and I would like to motivate them to take up mathematics as a major. They have seen Apostol's Calculus, some Linear Algebra (a la Hoffman & Kunze), and some Group theory (a la Herstein). ie. They are not unused to rigour, but might be a little daunted by too much of it.
Therefore, I would like to do some serious mathematics with them, but with a view to get them interested in geometry/topology (They chose this topic based on advice from some older students).
Some topics I had in mind were :
a) Wallpaper patterns/Platonic solids and their symmetry groups
b) Euler's theorem for polyhedra ($v-e+f = 2$)
c) A gentle introduction to the fundamental group
Could anyone suggest a good book to follow? I can only think of Armstrong's Basic topology, which I will follow in the absence of anything better, but some of you out there probably have some experience doing this (in summer math camps and such). Any suggestions?
Thanks.
 A: If you really mean general-topology, than I would recommend Set Theory and Metric Spaces, by Kaplansky.  This is an evergreen classic, and it is well-suited for a bright student to read mostly on her own and then discuss with others.  The exposition is extremely lucid and complete, and is usually followed by some interesting and challenging problems.  In fact I led an informal course on this with two friends of mine (physics / computer science types who were past college age but still very interested in mathematics) and it worked nicely.  
On the other hand, none of your examples are in general topology.  The first is geometry, and the latter two are algebraic topology.  In my experience if you compromise too much on "rigor" or "seriousness" in algebraic topology then you wind up staring at pictures and talking about glue.  On the other hand, a lot of the main texts on algebraic topology will be a bit forbidding for most undergraduates.*  One book which I enjoyed as an undergraduate and still looks very nice to me now is John Stillwell's Classical Topology and Combinatorial Group Theory.  In contrast to Kaplansky's text, most undergraduates would want some help and direction with this book, which would give you something to do.
*: "For a long time, books on algebraic topology were of two kinds: either they ended with the Klein bottle, or they were written in the style of a letter to Norman Steenrod."  -- Giancarlo Rota
A: Intuitive Combinatorial Topology by V.G. Boltyanskii, V.A. Efremovich covers these topics.
Also there is First Concepts of Topology by William G. Chinn, Norman Earl Steenrod.
A: For point set topology, by far the most popular book is Topology by Munkres.
It is a very easy read. Other reference is Basic topology by Jones and bartlet publisher. I forgot the author's name.
Yet another book is essential topology published by springer in its undergraduate series. Again I forgot the author.
A: I haven't taught from it, but Topology Now! by Robert Messer and Philip Straffin seems like a nice introduction. They bring in knots and links right from the start, which should appeal to many students.  
A: This one may be a bit more than what you need; but is a superb book regardless: Singer and Thorpe's "Lecture notes on topology and geometry". It starts with basic general topology and goes on to fundamental group and simplicial complexes and later to manifolds and de Rham's theorem and ends with a small dose of Riemannian geometry(geodesics, etc). This can be a 1 year reading course for a bright undergraduate.
Next is in regards to:

if you compromise too much on "rigor" or "seriousness" in algebraic topology then you wind up staring at pictures and talking about glue. 

If the rigorous definitions of deformation retract, homotopy equivalence etc. are learned from somewhere appropriate(such as Armstrong), then V. V. Prosolov's "Intuitive Topology" is an excellent book to motivate oneself into topology.
