Way back in 1980 I took a course at Oberlin College from Professor Henle in which he used this book (his own) as the text. Up until then I had been wavering as to a major, whether it should be in the hard sciences or Math. Michael Henle, his course, and this textbook decided me. I majored in Math.
The book gives a very hands on, concrete approach to what is a very abstract realm. An example that comes immediately to mind is the proof of the classification of manifolds, which comes down to a sequence of clever cut and paste operations on a large sheet with labeled edges. This text also has a curious sense of humor subtly hidden through it. Just look in the index under 'Man in the moon'. I dare you!
The exercises, which consist mostly of writing proofs, where there is very little notation and all your ideas have to be written out long-hand, are incredibly valuable for developing a logical mind. At least they were for me, back in 1980.
I think this is Dover Publications best title in topology.There is a fantastic and thorough introduction to many ofthe finer theorems (e.g.: Brouwer's Fixed Point Theorem, Sperner's Lemma, etc.). I was absolutely captivated with the ease with which Dr. Henle explained some remarkably difficult concepts. Much time is spent on some of the more unusual topics for a text at this level, including homology and even the qualitative behavior of differential equations! A serious book, for advanced undergraduates and graduates. Very enriching, and a definite plus as a reference tool.
Ignore those that suggest this book is too "elementary". This is a wonderful text that concretizes the more abstract notions of algebraic topology. True, it should not be your only text on algebraic topology, and the proofs are not as rigorous as a pedant might want, but it clearly conveys the geometric underpinnings of topology and deserves a space on any topologist's bookshelf.
Leicht verständlich,regt zum nachdenken an,fast wie ein rätsel. Sehr guter einleitender Text, allerdings nicht alle "Basics" enthalten. Ersetzt somit weitere Grundlektüre nicht, macht diese aber sehr viel einfacher verständlich.
I believe the two existing reviews are over-ratng. True, the book is accessible to anyone without prior knowledge of topology/algebra, but the treatment is too "elementary". For example, the author doesn't even introduce the word "mod 2 homology". If you are resolutely to study algebraic (or differential) topology, this is NOT the book to "study". Try Bredon or Fomenko-Novikov or May. For the subject covered, look for the book by Stillwell.