  These are the notes for a lecture series on Heegaard Floer homology, given by
the first author at the R\'enyi Institute in January 2023, as part of a special
semester titled ``Singularities and Low Dimensional Topology''. Familiarity
with Heegaard diagrams and Morse theory is assumed. We first illustrate the
relevant algebraic structures via grid homology, and then highlight the
geometric rather than combinatorial nature of the general theory. We then
define Heegaard Floer homology in the context of Lagrangian Floer homology, and
describe some key properties.
