Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc. This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level. One main feature is the treatment of both continuous and discrete optimization at the same place. This allows to study the problems under different points of view, supporting a better understanding of the entire field. The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course; however, each of its parts can also be taught separately. Many exercises are included to increase the reader's understanding.