This work is a collection of the original papers presented at an international colloquium concerned with "Vector Bundles on Algebraic Varieties" held at the Tata Institute of Fundamental Research, Bombay, in 1984. The purpose of the colloquium — and of this authoritative volume — is to highlight recent developments in the general area of vector bundles as well as principal bundles on both affine and projective varieties. Among the topics discussed are projective modules and quadratic spaces over general rings. Researchers in mathematics and physics will value this insightful presentation.