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The search for novel phases in strongly correlated systems is one of the most active frontiers in contemporary condensed matter physics. In this thesis the author explores the ground state phases of correlated electrons in one-dimension, modelled by the extended Hubbard model at half-filling, focusing on the novel bond-order-wave phase at small to intermediate couplings - a previously unknown phase whose existence was conclusively established by the author and his co-workers. The second problem studied involves the Peierls transition in correlated electrons interacting with finite frequency...