This is actually Volume I of the five-volume series. Typerset on a typewriter, but the writing is great. Great introduction to manifolds, metrics, Lie groups, and some algebraic topology. A classic.

A Comprehensive Introduction to Differential Geometry Volume Two

Science & Math

Spivak, Michael

Mathematics

Publish or Perish

Spivak's 5 volume set is a classic and overall the best and most thorough treatment of differential geometry

A Comprehensive Introduction to Differential Geometry. Volume Four

Michael Spivak

Spaces of Constant Curvature

Wolf, Joseph A.

Joseph Albert Wolf

The Atiyah-Singer Theorem and Elementary Number Theory (Mathematics Lecture No. 3)

Hirzebruch, F.

Zagier, D.

The Index Theorem and the Heat Equation

Gilkey, Peter B., and Sacks, Jon

A short course in fluid mechanics (Mathematics lecture series ; 6)

Thomas J.R. Hughes

Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. 
Besides providing a guide to understanding knot theory, the book offers "practical" training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements. It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. 
Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included.

Knots and Links

Rolfsen, Dale

Lectures on minimal submanifolds (Mathematics lecture series ; 9)

Lawson, H. Blaine

Real Algebraic Differential Topology (Mathematics Lecture Series, 10)

Palais, Richard S.

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