Differential geometry as a tool for applied mathematicians -- Some heuristic comments on solitons, integrability conditions and lie groups -- On Bäcklund transformations and solutions to the 2+1 and 3+1 - dimensional sine - Gordon equation -- Bäcklund transformations -- Generalised Bäcklund transformations for integrable evolution equations associated with Nth order scattering problems -- Meromorphic forms solutions of completely integrable Pfaffian systems with regular singularities -- Far fields, nonlinear evolution equations, the Bäcklund transformation and inverse scattering -- Convergence of formal power series solutions of a system of nonlinear differential equations at an irregular singular point -- Non-linear wave equations as hamiltonian systems -- How many jumps? Variational characterization of the limit solution of a singular perturbation problem -- The continuous Newton-method for meromorphic functions -- A precise definition of separation of variables -- Generation of limit cycles from separatrix polygons in the phase plane -- Normal solvability of linear partial differential operators in C?(?) -- Connection problems for linear ordinary differential equations in the complex domain -- Periodic solutions of continuous self-gravitating systems.