KdV and KP; Analytic Methods. Inverse Scattering. KdV on the Line. Problems in Mechanics and Hill's Equation. On the Geometry of KdV. Finite Zone Potentials. Hamiltonian Theory for KdV. Determinant Methods for KdV and KP; Tau Functions. Systems and Algebraic Methods. Orbits of the Vacuum. AKNS Systems. Some Lie Theoretic Methods. The Hirota Bilinear Identity. Algebraic Curves and KP. Introductory Sato Theory. Physics. Holonomic Quantum Fields. Ising Model and Bose Gas. Some remarks on 2-D Quantum Gravity and KdV. Conformal Field Theory. More on Conformal Field Theory and Tau Functions. More on Kricever Data, Grassmannians, Curves etc. Remarks on Strings. More on Strings, Riemann Surfaces, and Tau Functions. Remarks on Tau Functions, Cauchy-Riemann Operators, and Determinant Bundles. Quantum Inverse Scattering. Appendices: Differential Geometry and Elementary Hamiltonian Theory. Riemann Surfaces and Algebraic Curves. References. Index.