VLSI (very large scale integration) is a magic acronym in modern science and technology. Amongst other strik- ing aspects this field has turned out to be an excellent arena for applications of discrete mathematics and combinatorial optimization. The contributions to this volume, covering a wide range of research in this important field, develop from lectures delivered at a scientific meeting focused on paths, flows and VLSI-layout, held in Bonn in the summer 1988. The speakers, including several of the most prominent researchers in the field, were asked to formalize and extend their lectures into written surveys, giving a complete account of their topics. The volume will serve as a compendium demonstrating the liveliness of the area, as well as indicating directions for future work.