Higher Mathematics - Lectures Part One includes the first 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 winter semester 1981/82 at the Technische Universität München where he attended the respective lecture course held by Prof. Dr. Armin Leutbecher. The nine chapters of this volume provide introductions to fundamental concepts of mathematics such as: complete mathematical induction; inequalities and absolute value; limit values and differentiation; important functions such as exponential, logarithm, and power functions as well as polynomials; existence theorems with special emphasis on applications of the mean value theorem; oscillation equation and trigonometric functions; affine transformations in the plane; and complex numbers.