This book introduces Maple in a rather special way; namely, it shows how a computer algebra system most naturally fits into a mathematically oriented work environment. The intended audience is the mixed group of mathematicians, econometricians, engineers and other scientists, principally those who in their chosen discipline need to work with mathematical ideas and techniques. The book distinguishes itself from existing ones in the following ways: - It instructs the reader about the use of Maple by posing problems of a strictly mathematical nature. - It is intended not as a mere introduction to Maple, but also to show how Maple - and other computer algebra systems - may enrich our knowledge and deepen our understanding of mathematics. In that respect it focusses on mathematics rather than on Maple. In doing this it tries to convince scientists who are not naturally inclined to incorporate the computer into their daily work routine that a computer algebra system may very well enhance their theoretical work.