Explore pseudo-reductive groups in this 56-minute lecture by Brian Conrad from Stanford University. Delve into the intricacies of Zariski-dense subgroups and number-theoretic techniques in Lie groups and geometry. Begin with an introduction to sample situations and key definitions before uncovering the "magic lemma" and its properties. Examine field extensions, construction methods, and important theorems related to pseudo-reductive groups. This talk is part of a special online event organized by the International Centre for Theoretical Sciences, featuring contributions from Professor Gopal Prasad in various areas of mathematics.