Explore advanced concepts in applied model theory with this lecture by Zoé Chatzidakis from CNRS - ENS. Delve into topics such as risky closures, risky density, algebraic closure, algebraic groups, algebraic subgroups, and PAC fields. Gain a deeper understanding of the PAC Fields Theorem and its implications in the field of model theory. This 1 hour and 34 minute presentation, part of the Fields Institute's series on Topics in Applied Model Theory, offers a comprehensive exploration of these complex mathematical concepts for researchers and advanced students in the field.