This textbook is a clear, self-study suitable introduction to Operations Research and covers fundamental mathematical algorithms and problems of linear and nonlinear optimization. The main topics include the Simplex method and duality, as well as Lagrange multipliers and Karush-Kuhn-Tucker conditions. Numerous exercises and exam problems with complete solutions facilitate understanding and motivate the practice of the explained mathematical concepts. The theory is consistently illustrated with examples, intentionally omitting detailed proofs and mathematical rigor. Compact summaries help to quickly grasp the truly important aspects. The book serves as a compact companion for a lecture and also supports efficient exam preparation.