This volume consists of articles based on lectures delivered at an International Colloquium held at the Tata Institute of Fundamental Research, Bombay. Experts from all over the world spoke at the Conference on different aspects of geometry and analysis. Topics impact of geometry on the boundary solutions of a semilinear Neumann problem with critical nonlinearity; algebraic representations of reductive groups over local fields; scalar conservation laws with boundary condition; and the Borel-Weil theorem and the Feynman path integral.