1 Generalized Solutions to Monge-Ampere Equations. - 1. 1 The normal mapping. - 1. 2 Generalized solutions. - 1. 3 Viscosity solutions. - 1. 4 Maximum principles. - 1. 5 The Dirichlet problem. - 1. 6 The nonhomogeneous Dirichlet problem. - 1. 7 Return to viscosity solutions. - 1. 8 Ellipsoids of minimum volume. - 1. 9 Notes. - 2 Uniformly Elliptic Equations in Nondivergence Form. - 2. 1 Critical density estimates. - 2. 2 Estimate of the distribution function of solutions. - 2. 3 Harnack's inequality. - 2. 4 Notes. - 3 The Cross-sections of Monge-Ampere. - 3. 1 Introduction. - 3. 2 Preliminary results. - 3. 3 Properties of the sections. - 3. 4 Notes. - 4 Convex Solutions of det D2u = 1 in ?n. - 4. 1 Pogorelov's Lemma. - 4. 2 Interior Hölder estimates of D2u. - 4. 3 C?estimates of D2u. - 4. 4 Notes. - 5 Regularity Theory for the Monge-Ampère Equation. - 5. 1 Extremal points. - 5. 2 A result on extremal points of zeroes of solutions to Monge-Ampère. - 5. 3 A strict convexity result. - 5. 4 C1?regularity. - 5. 5 Examples. - 5. 6 Notes. - 6 W2pEstimates for the Monge-Ampere Equation. - 6. 1 Approximation Theorem. - 6. 2 Tangent paraboloids. - 6. 3 Density estimates and power decay. - 6. 4 LP estimates of second derivatives. - 6. 5 Proof of the Covering Theorem 6. 3. 3. - 6. 6 Regularity of the convex envelope. - 6. 7 Notes. Language: English