Henry Adams and Enrique Alvarado: An introduction to Morse theory

We give an introduction to Morse theory. Given a space equipped with a real-valued function, one can use Morse theory to produce a compact cellular model for that space. Furthermore, the cellular model reflects important properties of the function. We describe CW cell complexes, the Morse lemma, the two main theorems of Morse theory, Morse complexes, Morse-Smale complexes, and simplifications of Morse complexes.