The Advanced Computing Research Institute (ACRI) is a unit of the Cornell Theory Center and is affiliated with the Cornell Computer Science Department. The ACRI is concerned with research in scientific computation and its application to engineering and scientific problems with the emphasis on the use and potential of advanced computer architecture and environments. Research areas include restructuring compilers for scientific computation, and the design of algorithms for numerical linear algebra, optimization, and differential equations. Currently, ACRI researchers are collaborating on several large-scale applications in the computational sciences, including: protein-folding and related molecular chemistry problems, structural optimization and biomechanics, particle methods for turbulent combustion, discrete-control problems, and the application of boundary elementmethods. The parallel computers available to ACRI for research include the Theory Center machines - a 128-node KSR computer, a 64-node IBM SP, and a network of IBM RS/6000s. This report contains a short summary of the progress made in the last year on each of the four main projects: parallelizing compilers, computational linear algebra, computational optimization, and numerical methods for partial differential equations. Included also are a list of ACRI researchers and their research interests, a list of technical reports produced this last year, and a list of ACRI seminars.