  Link Floer homology is an invariant for links defined using a suitable
version of Lagrangian Floer homology. In an earlier paper, this invariant was
given a combinatorial description with mod 2 coefficients. In the present
paper, we give a self-contained presentation of the basic properties of link
Floer homology, including an elementary proof of its invariance. We also fix
signs for the differentials, so that the theory is defined with integer
coefficients.
