This conference was held at the Mathematical Research Institute in Oberwolfach from 30 November to 6 December 1986 under the direc- tion of J. Albrecht (Clausthal-Zellerfeld), L. Collatz (Hamburg), W. Velte (Wlirzburg) and W. Wunderlich (Bochum). Focal points during the meeting were eigenvalue problems in the engineering sciences and in industry, methods for calculating bounds for eigenvalues, and matrix eigenvalue problems. Central to the lectures on eigenvalue problems pertinent to the engineering sciences and industry were oscillation and stability problems; for these, numerical treatment drew mainly on finite- element methods in the lectures as well as in the ensuing discus- sions, questions concerning the quality of the mathematical models applied, and the choice of appropriate finite elements, were given wide latitude. Other lectures addressed new research results in the calculation of (primarly lower) bounds for eigenvalues. The ramifications of these results were illustrated by numerous examples taken from fields in the engineering sciences and physics. The extensive use of finite-element methods (made possible in the wake of major computer advances) has led to new research in matrix eigenvalue problems, and several lectures reported on results which have been achieved in this area.