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Note to instructors and students

in The lectures contain numerous examples and exercises all of which need not be worked through in detail. It is entirely up to the instructor to select a few for illustration in class and assign a few as home assignments. Complete solutions are provided for any exercise that is referred to in the proof of any theorem. In fact solutions to more than half of the exercises are available on line and hints (beyond what has already been indicated against the exercise) are provided for many others.

Depending on the availability of time and the background of the class the instructor may choose to omit some topics altogether. For instance if the class is not well-prepared in general topology the instructor may wish to spend more time on the material covered in the first five lectures and leave out some of the later sections of the first part or discuss them superficially. Another route is to work thorough the first part throughly and leave out some of the technical proofs in the second part. In fact some basic courses on algebraic topology cover only the theory of covering spaces and fundamental groups but this would involve discussing thoroughly the existence of a universal cover and the Galois theory of covering spaces not discussed here. The text of W. Massey may be used as a supplementary reference for these topics. Beyond these broad hints we offer no specific suggestions on what to cover/omit and leave this choice to the instructor.

The examples have been worked out in meticulous detail in order to encourage students to write out clear proofs and adhere to standard levels of mathematical rigor. Hand waving is unfortunately much too common in algebraic topology and often one finds students offering specious arguments. The material is intended for forty one hour sessions six of which are to be used for one hour tests. Some longer topics have been assigned two lectures.

Perhaps more pictures are desirable. We encourage the reader to doodle (preferably with coloured pencils) as he/she goes along drawing relevant figures and diagrams. Lovely pictures of the Klein's bottle and other things are available on the internet and readers who have access to the internet that we encourage the reader to explore.