This short course aims to give a brief introduction to Heegaard Floer (HF) homology, a theory pioneered in the last decade by Peter Ozsvath and Zoltan Szabo, with an emphasis on applications. In brief, Heegaard Floer homology is an invariant of 3-manifolds and 4-dimensional cobordisms between them; there is a related invariant for links in 3-manifolds which was developed independently by Jake Rasmussen. In recent years, these invariants have led to tremendous progress on problems in low-dimensional topology. After sketching the apparatus of the theory, we will focus on a few specific topics: (1) knot surgeries that give lens spaces (the Berge conjecture); (2) the four-ball genus of a knot; (3) the unknotting number of a knot; and (4) quasi-alternating links. Which waters we will chart will depend on the audience's interest.