Algebraic Topology by Allen Hatcher 2001

In most major universities one of the three or four basic first-year graduate
mathematics courses is algebraic topology. This introductory text is suitable
for use in a course on the subject or for self-study, featuring broad coverage
and a readable exposition, with many examples and exercises. The four main
chapters present the basics: fundamental group and covering spaces, homology
and cohomology, higher homotopy groups, and homotopy theory generally.
The author emphasizes the geometric aspects of the subject, which helps
students gain intuition. A unique feature is the inclusion of many optional
topics not usually part of a first course due to time constraints: Bockstein
and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf
algebras, the Brown representability theorem, the James reduced product,
the Dold-Thom theorem, and Steenrod squares and powers.

Differential Topology Allan Pollack and Victor Guillemin 1974

This text fits any course with the word "Manifold" in the title.
It is a graduate level book.

Topology by James Munkres 2nd Edition 2000

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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