Learn the Spectral Theorem in this 54-minute lecture delivered by Oscar Reula from the National University of Córdoba, Argentina, as part of the ICTP-SAIFR Minicourse on Partial Differential Equations: Analytical and Numerical Tools. Explore the fundamental mathematical concepts underlying the spectral theorem and its applications in the context of partial differential equations. Gain insights into the theoretical foundations that connect linear algebra and functional analysis to the study of differential equations, building upon the analytical and numerical tools framework established throughout this comprehensive minicourse series.