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A major goal of large-scale structure studies is to determine the properties of the initial conditions that ``seeded'' the formation of galaxies, clusters, and superclusters. The traditional approach to this problem is based on a purely statistical comparison between predictions of theoretical models and observed galaxy clustering. A complementary approach is to work backwards from present-day structure to a model of the initial fluctuations in the same region of space. I will summarize two different schemes for reconstructing initial condtions, one based on the assumption that the primordial fluctuations were Gaussian, and one based on reversible dynamical approximations for mildly non-linear gravitational evolution. Each scheme has its advantages, and a hybrid method could combine the best features of both. I will discuss what things we might learn about structure formation from the reconstruction approach.
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