The course focuses on basic mathematical models and methods for solving optimization engineering problems, especially computer support for modeling and solving using appropriate software. The course has been inspired by the author's experience with similar courses at foreign universities (Computer-Aided Optimization). It is also suitable for students who are interested in solving similar problems regardless of their specialization and year of study. Emphasis is placed on examples of solutions to typical problems, including problems solved within the framework of BUT and FME projects. Specific assignments are then solved using appropriate software from different areas (MS Excel, MATLAB, GAMS, etc.). The general principles of mathematical model building are systematically followed: problem formulation and analysis, building a mathematical model, classification of the model and use of its theoretical properties, appropriate model transformation, algorithmic solution, analysis and interpretation of the obtained solution. The course includes examples of solving optimization models that are linear, network-based, nonlinear and integer.