These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.

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John Milnor is one of the most distinguished mathematicians of our time, and has been awarded the Fields Medal, the Wolf Prize, the Abel Prize, and all three Steele prizes. He is a Distinguished Professor of Mathematics at Stony Brook University. He previously taught at Princeton University and was on the faculty of the Institute for Advanced Study in Princeton.

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