The development and computational implementation of analytical expres- sions for the low-order derivatives of electronic energy surfaces and other molecular properties has undergone rapid growth in recent years. It is now fairly routine for chemists to make use of energy gradient information in locating and identifying stable geometries and transition states. The use of second analytical derivative (Hessian or curvature) expressions is not yet routine, and third and higher energy derivatives as well as property (e.g., dipole moment, polarizability) derivatives are just beginning to be applied to chemical problems. This NATO Advanced Research Workshop focused on analyzing the re- lative merits of various strategies for deriving the requisite analyti- cal expressions, for computing necessary integral derivatives and wave- function parameter derivatives, and for efficiently coding these expres- sions on conventional scalar machines and vector-oriented computers. The participant list contained many scientists who have been instrumen- tal in bringing this field to fruition as well as eminent scientists who have broad knowledge and experience in quantum chemistry in general.