Higher Mathematics - Lectures Part Four includes the fourth semester material of a four-semester lecture course on higher mathematics as it is obligatory in many study courses for natural and engineering sciences at German universities. The content selection in this volume was based on the lecture notes the author took during the summer semester 1983 at the Technische Universität München where he attended the respective lecture course held by Prof. Dr. Armin Leutbecher. The seven chapters of this volume provide introductions to the following concepts of mathematics: Elementary Solution Methods for Ordinary Differential Equations; Boundary Value Problems of Ordinary Differential Equations; Inversive Geometry and Number Sphere; Holomorphic or Analytic Functions; Integration of Complex-valued Functions; Theory of Analytic Functions; and Applications of the Residue Theorem.