Dive into a comprehensive 4.5-hour video series on functional analysis, exploring key concepts from metric spaces to spectral theory. Begin with the fundamentals of metric spaces, open and closed sets, and sequences. Progress through norms, Banach spaces, and Hilbert spaces, examining important theorems like Cauchy-Schwarz Inequality and Riesz Representation. Investigate continuity, bounded operators, and compact sets, including the Arzelà–Ascoli theorem. Delve into advanced topics such as Hölder's and Minkowski inequalities, dual spaces, and pivotal principles like the Uniform Boundedness Principle and Hahn-Banach theorem. Conclude with an in-depth exploration of spectral theory, covering the spectrum of bounded operators, multiplication operators, and properties of normal and self-adjoint operators.