  We develop algebro-geometrical approach for the open Toda lattice. For a
finite Jacobi matrix we introduce a singular reducible Riemann surface and
associated Baker-Akhiezer functions. We provide new explicit solution of
inverse spectral problem for a finite Jacoby matrix. For the Toda lattice
equations we obtain the explicit form of the equations of motion, the
symplectic structure and Darboux coordinates. We develop similar approach for
2D open Toda. Explaining some the machinery we also make contact with the
periodic case.
