​ Our aim is to find new (generalized) Lie systems and new superposition rules, also for PDEs and higher order equations.  Studying discretizations compatible with superposition rules will lead to geometric integrators which can be used for numerical methods of finding solutions. We want to include also quantum Lie systems, based on Lie algebras of selfadjoint operators on a Hilbert space (Schroedinger operators). Our main objectives concern:

 - Lie systems compatible with geometric structures.

 - Discretization, randomization and quantization.

 - Symmetries, integrability and other application of Lie theory.

 - Super-Lie systems and Lie superalgebras of super-vector fields.