Laplace transformations (for continuous problems) and z-transformations (for discrete problems) are important parts of the mathematical background required for engineers, physicists and mathematicians, particularly for solving classes of differential and difference equations. The first two chapters present the theory and basic properties of these transformations. The next two chapters offer a “User’s Guide” for the Mathematica package developed by the author. As seen from the remaining two thirds of the book, the package substantially enhances the built-in facilities of Mathematica and includes algorithms for the numerical inversion of Laplace transforms. The emphasis lies on computational and applied parts, particularly in the fields of control engineering, electrical engineering, and mechanics (heat conduction, diffusion, vibrations). Many examples from applied sciences and engineering illustrate the applicability of the theory and the use of the package. Students, instructors, practical engineers and researchers working in the field of control, electricity or mechanics, will find this textbook a most valuable source and will profit from the package and further examples and Mathematica notebooks on the included CD-ROM. The owner of the book is authorized to use the software on a single machine.