Computer algebra systems are widely used in pure and applied mathematics, physics, and other natural sciences, engineering, economics, as well as in higher and secondary education (see, e.g., [1–5]). For example, many important calculations in theoretical physics could never be done by hand, without wide use of computer algebra. Polynomial or trigonometric manipulations using paper and pen are becomingas obsolete as school long division in the era of calculators. There are several powerful general-purposecomputer algebra systems. The systemMathematicaismostpopular.Itcontainsahugeamountofmathematicalknowledge in its libraries. The fundamental book on this system [6] has more than 1,200 pages.Fortunately,thesame information(moreup-to-datethanina printedbook)is available in the help system and hence is always at the ?ngertips of any user. Many books about Mathematica and its application in various areas have been published; see, for example,the series [7–10] of fourbooks(each morethan 1,000pages long) or [11]. The present book does not try to replace these manuals. Its ?rst part is a short systematic introduction to computer algebra and Mathematica; it can (and should) be read sequentially. The second part is a set of unrelated examples from physics and mathematics which can be studied selectively and in any order. Having understood the statement of a problem, try to solve it yourself. Have a look at the bookto get a hint only whenyouget stuck. Explanationsin this part are quite short.