Course description: A self-contained introduction to the theory of soliton equations with an emphasis on its applications to algebraic-geometry. Topics include: 1. General features of the soliton systems. Basic hierarchies of commuting flows: KP, 2D Toda, Bilinear Discrete Hirota hierarchy. Discrete and finite-dimensional integrable systems. 2. Algebraic-geometrical integration theory. Spectral curves. Baker-Akhiezer functions. 3. Hamiltonian theory of soliton equations.