In this seminar, we will study the moduli spaces of the holomorphic discs. The moduli spaces of the holomorphic discs in toric Fano manifolds with boundary on torus fibers behave nicely because the standard complex structure is integrable. More specifically, we will show the Fredholm regularity of these holomorphic discs, which means that the moduli spaces of the holomorphic discs are smooth manifolds of expected dimensions.