The course presents fundamental mathematical models and methods for solving of optimization engineering problems. It is based on the author's experience with similar courses at the EU and US universities (Computer-Aided Optimization). It is suitable for students interested in the solution of such problems coming from various specializations and years of study. Examples of typical problems involve cases studied and solved within the framework of BUT and FME projects. Particular instances are solved by using a suitable software (MS Excel, Matlab, GAMS aj.). Modelling rules are systematicaly applied: problem formulation and analysis, model building and classification, the use of theory, transforamtions and algorithms, solution analysis and interpretation. The examples of linear, network, nonlinear, integer, dynamic and uncertain models are introduced.