  We review the construction of Heegaard Floer homology for closed
three-manifolds and also for knots and links in the three-sphere. We also
discuss three applications of this invariant to knot theory: studying the
Thurston norm of a link complement, the slice genus of a knot, and the
unknotting number of a knot. We emphasize the application to the Thurston norm,
and illustrate the theory in the case of the Conway link.
