The textbook provides a comprehensive yet practical look at optimization theory and applications, with examples and MATLAB programs. The author introduces concepts and methods with mathematical formulations followed by clear examples. The programs provided in MATLAB, inserted in text (being also downloadable), are useful for practicing the methods on the given examples, and for visualization of results. Topics covered include Linear Programming or Calculus of Variations, Quadratic Programming, Integer Programming, etc. After presenting basics, the book goes on to introduce further methodological steps, like Interior Point methods, Evolutionary approaches, Multi-objective Optimization and Decision-making (including Portfolio management), Games, and the application to sparse representations (also related to Machine Learning) and image processing. The reader can easily take initiative, exploring other examples or cases of own interest, by using/modifying the programs. The book is addressed to upper undergraduate and graduate students of engineering, mathematics and other sciences, computer studies, economics, and management.