Explore the major advancements in mathematical general relativity in this lecture by Sergiu Klainerman from Princeton University. Delve into the field's origins, tracing back to Y.C. Bruhat's groundbreaking Acta paper titled "Théorème d'existence pour certains systèmes d'equations aux dérivées partielles non-linéaires." Gain insights into the evolution of this complex subject over the past 72 years, examining key developments and their impact on our understanding of general relativity. Learn about the mathematical foundations that have shaped this field and how they continue to influence modern research in theoretical physics and cosmology.