Morse theory, conceived as the study of functions on manifolds, has a number of applications to geometry and topology. Many natural objects, such as geodesics, for example, arise as critical points (in particular, as minima) of a functional. Topics to be discussed include Morse functions, index, Morse lemma, Sard’s theorem, Morse inequalities, attaching handles, loop space of a manifold, energy functional. Primary applications involve conjugate points (leading to Myers’ theorem for example), determining cell decompositions (for computing Betti numbers, homology and homotopy groups), and mini-max constructions (leading to existence of certain geodesics). Depending on time and the interests of the class, additional topics might include Morse theory on singular spaces, further results on geodesics, Bott periodicity and/or outline of the proof of the Poincaré conjecture in dimensions ≥ 5.