Includes bibliographical references and index.

Automorphisms of the Weyl algebra and bispectral operators ; Huygens' principle and the bispectral problem ; Some bispectral musings ; Beyond the classical orthogonal polynomials ; Bispectral operators, dual isomondromic deformations and the Riemann-Hilbert dressing method ; Darboux transformations and the bispectral problem ; The discrete version of the bispectral problem ; Explicit formulas for the Airy and Bessel bispectral involutions in terms of Calogero-Moser pairs ; Bispectrality and Darboux transformations in the theory of orthogonal polynomials ; Baker-Akhiezer functions and the bispectral problem in many dimensions ; Bispectral algebras of ordinary differential operators ; The bispectral problem, rational solutions of the master symmetry flows, and bihamiltonian systems ; The geometry of spinors and the multicomponent BKP and DKP hierarchies ; The Hamiltonian route to Sato Grassmannian ; Darboux transformations in associative rings and functional-difference equations ; Remarks about the Calogero-Moser system and the KP equation