The main lectures and the supplemental lectures plan to address the following major themes: (1) the basic theory of nonlinear difference equations; (2) the connection between discrete integrable systems and continuous integrable systems; (3) the connection of geometry with discrete Painlevé equations, especially the ell-discrete Painlevé equation; (4) asymptotic analysis of discrete Painlevé equations; and (5) obtaining special solutions through elementary methods such as Hirota’s bilinear form and Bäcklund and other transformations.