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This volume contains 13 papers from the conference on 'Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory'. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S^1$ fixed points in Quot-schemes and mirror principle computations for Grassmannians by S.T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.