Optimal design of experiments is an essential component of any research that aims at the estimation of unknown parameters, at model validation, or at the comparison and selection of the best among several competing models. The authors' goals are to explain the basic ideas and to create interest in modern problems of experimental design. The topics discussed include designs for inference based on nonlinear models, designs for models with random parameters and stochastic processes, designs for model discrimination and incorrectly specified (contaminated) models, and examples of designs in functional spaces. As the authors avoid technical details, the book assumes only a moderate background in calculus, matrix algebra, and statistics. However, at many places, hints are given as to how the reader may enhance and adopt the basic ideas for advanced problems or applications. This will allow the book to be used for courses at different levels, and it will be a useful reference for graduate students and researchers in statistics and engineering.