Abstract
* Introduction* Knots and links in $S^3$* Grid diagrams* Grid homology* The invariance of grid homology* The unknotting number and $\tau$* Basic properties of grid homology* The slice genus and $\tau$* The oriented skein exact sequence* Grid homologies of alternating knots* Grid homology for links* Invariants of Legendrian and transverse knots* The filtered grid complex* More on the filtered chain complex* Grid homology over the integers* The holomorphic theory* Open problems* Homological algebra* Basic theorems in knot theory* Bibliography* Index
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