The mathematical modeling of phenomena and processes in the natural and engineering sciences, increasingly also in economics and medicine, often leads to differential equations. This book is dedicated to the classical and weak solution theory of boundary value problems for linear and nonlinear ordinary differential equations. Building on this, it addresses linear and nonlinear operator differential or evolution equations of the first order using classical, variational, and semigroup methods. Additionally, fundamental numerical methods are analyzed. The text provides an introduction to (functional) analytical methods and aims to prepare the reader for relevant monographs and research literature.