P-adic integration: Rationality and Igusa zeta function

This lecture covers the proof of Dwork's theorem and introduces p-adic manifolds in differential geometry. It also discusses Serre's classification of p-adic manifolds, p-adic integration, and the rationality of the Igusa zeta function. The lecture concludes with a detailed explanation of the relationship between the Igusa zeta function and monodromy conjectures.