Explore microlocal methods for operators with analytic coefficients in this comprehensive lecture delivered by Maciej Zworski at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into advanced mathematical concepts as part of the Thematic Programme on "Spectral Theory and Mathematical Relativity." Over the course of one hour and two minutes, gain insights into the intricate world of microlocal analysis and its applications to operators with analytic coefficients. Enhance your understanding of spectral theory and its connections to mathematical relativity through this in-depth presentation by a renowned expert in the field.