We present here the transcripts of lectures and talks which were delivered at the NATO ADVANCED STUDY INSTITUTE "Electronic Structure of Complex Systems" held at the State University of Ghent, Belgium during the period July 12-23, 1982. The aim of these lectures was to highlight some of the current progress in our understanding of the electronic structure of com­ plex systems. A massive leap forward is obtained in bandstructure calculations with the advent of linear methods. The bandtheory also profitted tremendously from the recent developments in the density functional theories for the properties of the interacting electron gas in the presence of an external field of ions. The means of per­ forming fast bandstructure calculations and the confidence in the underlying potential functions have led in the past five years or so to a wealth of investigations into the electronic properties of elemental solids and compounds. The study of the trends of the electronic structure through families of materials provided invaluable insights for the prediction of new materials. The detailed study of the electronic structure of specific solids was not neglected and our present knowledge of d- and f-metals and metal hydrides was reviewed. For those systems we also investi­ gated the accuracy of the one electron potentials in fine detail and we complemented this with the study of small clusters of atoms where our calculations are amenable to comparison with the frontiers of quantum chemistry calculations.