%0 Journal Article %T An introduction to knot Floer homology %A Ciprian Manolescu %J Mathematics %D 2014 %I arXiv %X This is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid diagrams, and a combinatorial description in terms of the cube of resolutions. We discuss the geometric information carried by knot Floer homology, and the connection to three- and four-dimensional topology via surgery formulas. We also describe some conjectural relations to Khovanov-Rozansky homology. %U http://arxiv.org/abs/1401.7107v1