This book is recommended to Readers who – besides having general philosophical interests – also wish to attain deeper understanding in the subject area by carrying out numerical simulations for simple representative paradigms in creative manner. For this purpose small sample programs are available in program languages that require only minimal skills in programming and need hardware commonly available by students and free or widely used software packages. The fundamental mathematical tools are summarized, expounded, and geometrically interpreted in strict relationship with the needs of practical applications, too.