The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frolicher structures in the formal Kadomtsev-Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras.
The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.