This textbook presents the essential parts of the modern theory of nonlinear partial
differential equations including the calculus of variations. After a short review of results
in real and functional analysis the author introduces the main mathematical techniques for
solving both semilinear and quasilinear elliptic PDEs and the associated boundary value
problems. Key topics include infinite dimensional fixed point methods the Galerkin method the
maximum principle elliptic regularity and the calculus of variations. Aimed at graduate
students and researchers this textbook contains numerous examples and exercises and provides
several comments and suggestions for further study.
