Exact solutions in gauge theory, general relativity, and their supersymmetric extensions -- Symmetries and solutions of the einstein equations -- Superposition of solutions in general relativity -- Gauge fields, gravitation and Kaluza-Klein theory -- Gravitational shock waves -- Soliton surfaces and their applications (soliton geometry from spectral problems) -- Completely integrable systems of evolution equations on KAC moody lie algebras -- Integrable lattice systems in two and three dimensions -- Isovectors and prolongation structures by Vessiot's vector field formulation of partial differential equations -- Hamiltonian flow on an energy surface: 240 years after the euler-maupertuis principle.