This is the proceedings volume of the symposium entitled 'Trends in Computer Algebra' held in Bad Neuenahr, May 19-21, 1987. Computer algebra is a very active research area on the borderline between mathematics and computer science, which will strongly influence mathematical and physical research in the near future. The intention of this symposium was to bring together specialists in computer algebra with researchers in related areas of mathematics and computer science as well as potential users of the developed tools and techniques in order to discuss present issues and future trends of this topic. The thirteen invited talks of the symposium were organized into the following groups: Languages and Systems, Symbolic Computations, Computing in Algebraic Structures, and Applications.