Peter S. Ozsváth, Princeton University, NJ.Andras I. Stipsicz, Renyi Institute of Mathematics, Budapest, Hungary.Zoltán Szabó, Princeton University, NJ.

• IntroductionKnots and links in $S^3$Grid diagramsGrid homologyThe invariance of grid homologyThe unknotting number and $\tau$Basic properties of grid homologyThe slice genus and $\tau$The oriented skein exact sequenceGrid homologies of alternating knotsGrid homology for linksInvariants of Legendrian and transverse knotsThe filtered grid complexMore on the filtered chain complexGrid homology over the integersThe holomorphic theoryOpen problemsHomological algebraBasic theorems in knot theoryBibliographyIndex

Peter S. Ozsváth, Princeton University, NJ.Andras I. Stipsicz, Renyi Institute of Mathematics, Budapest, Hungary.Zoltán Szabó, Princeton University, NJ.

• IntroductionKnots and links in $S^3$Grid diagramsGrid homologyThe invariance of grid homologyThe unknotting number and $\tau$Basic properties of grid homologyThe slice genus and $\tau$The oriented skein exact sequenceGrid homologies of alternating knotsGrid homology for linksInvariants of Legendrian and transverse knotsThe filtered grid complexMore on the filtered chain complexGrid homology over the integersThe holomorphic theoryOpen problemsHomological algebraBasic theorems in knot theoryBibliographyIndex

Peter S. Ozsváth, Princeton University, NJ.Andras I. Stipsicz, Renyi Institute of Mathematics, Budapest, Hungary.Zoltán Szabó, Princeton University, NJ.

• IntroductionKnots and links in $S^3$Grid diagramsGrid homologyThe invariance of grid homologyThe unknotting number and $\tau$Basic properties of grid homologyThe slice genus and $\tau$The oriented skein exact sequenceGrid homologies of alternating knotsGrid homology for linksInvariants of Legendrian and transverse knotsThe filtered grid complexMore on the filtered chain complexGrid homology over the integersThe holomorphic theoryOpen problemsHomological algebraBasic theorems in knot theoryBibliographyIndex