In September 1989, a NATO Advanced Research Workshop on "Continuation and BIfurcations: NumerIcal TechnIques and Applications" was held at the Katholieke Unlversiteit Leuven, Belgium. Participants came from 10 countries in Europe and North America and were mainly from universities and research institutes. This proceedings volume contains 26 of the 38 papers which were presented at the meeting. Abstracts of most other contrIbutions are also included. The central theme of the workshop was the solution of parameter dependent nonlinear problems using numerical continuation. More specifically the aims can be stated as: to descrIbe typIcal bifurcation problems In sclentiftc, engineering and industrial problems; to discuss current mathematical ideas and new developments in numerical analysis and numerical techniques and to describe and evaluate program packages and to discuss future needs with respect to software. The interests of the participants extended over the complete spectrum of theory, numerical analysis, software and applications, and this spread is reflected both in the composition of this volume and in several of the papers. For example, there are contributions on the application of Centre ManIfold and Uapunov Schmidt theory to derive low dimensional systems which can be analysed by normal form theory for dynamical systems or singularIty theory."