Includes bibliographical references.

Backlund transformations of the higher order Painleve equations ; Dressing method and Backlund and Darboux transformations ; The classical geometry of Backlund transformations. Introduction to applications in soliton theory ; An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization ; On Bianchi and Backlund transformations of two dimensional surfaces in four dimensional Euclidean space ; Group invariant solutions without transversality and the principle of symmetric criticality ; Multi-component matrix KP hierarchies as symmetry-enhanced scalar KP hierarchies and their Darboux-Backlund solutions ; The Darboux-Backlund transformation and Clifford algebras ; On discrete Painleve equations as Backlund transformations ; A Backlund transformation for timelike surfaces of constant mean curvature in mathbb R^1,2 ; On Ribaucour transformations ; The Ribaucour congruences of spheres within Lie sphere geometry ; Backlund transformations for the reduced Maxwell-Bloch equations ; Transformations of quasilinear systems originating from the projective theory of congruences ; Backlund links between different analytic descriptions of constant mean curvature surfaces ; On the integrability of Weingarten surfaces ; A new immersion formula for surfaces on Lie algebras and integrable equations ; Difficulties with the SDiff(2) Toda equation ; Superposition formulas based on nonprimitive group action ; Symmetries of differential difference equations and Lie algebra contractions ; Backlund transformations from the bilinear viewpoint ; Towards the Lax formulation of SU(2) principal models with nonconstant metric ; Transcendental solutions of the sine-Gordon equation ; Three dimensional skyrmions and harmonic maps ; Induced surfaces and their integrable deformations ; Properties of a class of slowly decaying oscillatory solutions of KdV ; Blending two discrete integrability criteria: Singularity confinement and algebraic entropy ; Backlund transformations of soliton systems from symmetry constraints ; Open problems for the super KdV equations ; Combinatorial aspects of the Darboux transformation ; Backlund transformation and nonlinear superposition formula of the Kaup-Kupershmidt and Tzitzeica equations ; Classification of symmetry-integrable evolution equations ; Integrability of evolution equations and pseudo-spherical surfaces ; Infinitesimal Backlund transformations of nets. The 2 + 1-dimensional Sinh-Gordon system ; Isothermic surfaces and the Calapso equation: The full Monty ; Backlund transformations induced by symmetries. Application: Discrete mKdV ; Darboux transformation for a spectral problem quadratic in the spectral parameter ; Separation of variables and Darboux transformations ; Backlund transformations as nonlinear ordinary differential, or difference equations with superposition formulas