In this memoir, we prove that the universal Teichmüller space (T(1)) carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of (T(1)) -- the Hilbert submanifold (T_{0}(1)) -- is a topological group. We define a Weil-Petersson metric on (T(1)) by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that (T(1)) is a Kähler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmüller curve fibration over the universal Teichmüller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmüller spaces from the formulas for the universal Teichmüller space. We study in detail the Hilbert manifold structure on (T_{0}(1)) and characterize points on (T_{0}(1)) in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators (B_{1}) and (B_{4}), associated with the points in (T_{0}(1)) via conformal welding, are Hilbert-Schmidt. We define a "universal Liouville action" -- a real-valued function ({mathbf S}_{1}) on (T_{0}(1)), and prove that it is a Kähler potential of the Weil-Petersson metric on (T_{0}(1)). We also prove that ({mathbf S}_{1}) is (-tfrac{1}{12pi}) times the logarithm of the Fredholm determinant of associated quasi-circle, which generalizes classical results of Schiffer and Hawley. We define the universal period mapping (hat{mathcal{P}}: T(1)rightarrowmathcal{B}(ell^{2})) of (T(1)) into the Banach space of bounded operators on the Hilbert space (ell^{2}), prove that (hat{mathcal{P}}) is a holomorphic mapping of Banach manifolds, and show that (hat{mathcal{P}}) coincides with the period mapping introduced by Kurillov and Yuriev and Nag and Sullivan. We prove that the restriction of (hat{mathcal{P}}) to (T_{0}(1)) is an inclusion of (T_{0}(1)) into the Segal-Wilson universal Grassmannian, which is a holomorphic mapping of Hilbert manifolds. We also prove that the image of the topological group (S) of symmetric homeomorphisms of (S^{1}) under the mapping (hat{mathcal{P}}) consists of compact operators on (ell^{2}). The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).

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