This title investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. Aiming to provide an introduction to the topic, the text requires only basic pre-requisites. Rather than attempting to be encyclopedic, it illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.