Algebro-geometric Quasi-periodic Finite-gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Introduction The Toda hierarchy, recursion relations, and hyperelliptic curves The stationary Baker-Akhiezer function Spectral theory for finite-gap Jacobi operators Quasi-periodic finite-gap solutions of the stationary Toda hierarchy Quasi-periodic finite-gap solutions of the Toda hierarchy and the time-dependent Baker-Akhiezer function The Kac-van Moerbeke hierarchy and its relation to the Toda hierarchy Spectral theory for finite-gap Dirac-type difference operators Quasi-periodic finite-gap solutions of the Kac-van Moerbeke hierarchy Hyperelliptic curves of the Toda-type and theta functions Periodic Jacobi operators Examples, $g-0,1$ Acknowledgments Bibliography.