For several years now I have been teaching courses in computer algebra
at the Universitat Linz, the University of Delaware, and the Universidad
de Alcala de Henares. In the summers of 1990 and 1992 I have organized
and taught summer schools in computer algebra at the Universitat Linz.
Gradually a set of course notes has emerged from these activities.
People have asked me for copies of the course notes, and different
versions of them have been circulating for a few years. Finally I
decided that I should really take the time to write the material up in a
coherent way and make a book out of it. Here, now, is the result of this
work. Over the years many students have been helpful in improving the
quality of the notes, and also several colleagues at Linz and elsewhere
have contributed to it. I want to thank them all for their effort, in
particular I want to thank B. Buchberger, who taught me the theory of
Grabner bases nearly two decades ago, B. F. Caviness and B. D. Saunders,
who first stimulated my interest in various problems in computer
algebra, G. E. Collins, who showed me how to compute in algebraic
domains, and J. R. Sendra, with whom I started to apply computer algebra
methods to problems in algebraic geometry. Several colleagues have
suggested improvements in earlier versions of this book. However, I want
to make it clear that I am responsible for all remaining mistakes.