This book is a slightly augmented version of a set of lec- tures on optimization which I held at the University of Got- tingen in the winter semester 1983/84. The lectures were in- tended to give an introduction to the foundations and an im- pression of the applications of optimization theory. Since in- finite dimensional problems were also to be treated and one could only assume a minimal knowledge of functional analysis, the necessary tools from functional analysis were almost com- pletely developed during the course of the semester. The most important aspects of the course are the duality theory for convex programming and necessary optimality conditions for nonlinear optimization problems; here we strive to make the geometric background particularly clear. For lack of time and space we were not able to go into several important problems in optimization - e. g. vector optimization, geometric program- ming and stability theory. I am very grateful to various people for their help in pro- ducing this text. R. Schaback encouraged me to publish my lec- tures and put me in touch with the Vieweg-Verlag. W. BrUbach and O. Herbst proofread the manuscript; the latter also pro- duced the drawings and assembled the index. I am indebted to W. LUck for valuable suggestions for improvement. I am also particularly grateful to R. Switzer, who translated the German text into English. Finally I wish to thank Frau P. Trapp for her Gare and patience in typing the final version.