This book provides a coherent, self-contained introduction to central topics of Analytic Partial Differential Equations in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier-Bros-Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to existence and regularity questions. The book begins by establishing the fundamental properties of analytic partial differential equations, starting with the Cauchy-Kovalevskaya theorem, before presenting an integrated overview of the approach to hyperfunctions via analytic...