The monograph contains the description of physical models leading to some partial differential equations with applications. Both linear and nonlinear equations are considered. For each differential equation the main existing features are highlighted and complemented with examples and exercises. Preliminarly, a quick survey of the needed functional analytical tools is given: Sobolev spaces, the Lax-Milgram Theorem, the Galerkin method. Filippo Gazzola is professor at the Politecnico di Milano. He authored more than 160 articles published in international mathematical journals, 4 scientific monographs, 3 didactic books. Awarded with the Gaetano Fichera Price for research and with the Teaching Award of the Bocconi University for didactics. Member of the editorial board of the Journal of the European Mathematical Society and 3 other mathematical journals. Responsible of several research groups, among others "Fluid-structure interactions of the MUR Excellence Department".