The theory of functions is presented in this introduction in a completely new way. After a brief text section, each chapter includes the underlying theories and carefully selected examples. This is followed by a worksheet section that connects the theory of functions with computer applications and Maple. In sophisticated Maple worksheets, impressive graphics illustrate application examples from various fields. The book also demonstrates how ideas can be designed and implemented using a computer algebra system. This introduction to the theory of functions represents a new teaching format, rather than a classical presentation. The book bridges the gap to computer applications and Maple, which influences the structure of the individual chapters. In a text section, the underlying theory is presented—sometimes only in outline form—and supplemented with carefully selected examples.