The project is aimed at research in the field of stochastic partial differential equations (SPDEs), in particular, at the qualitative behaviour of solutions and optimal control thereof. Also, some related space-time systems (Brownian web) arising as a continuum limit of discrete random systems will be studied. More specifically, the following topics will be emphasized: 1. Non - Markovian SPDEs, in which the driving noise is a general Volterra process that does not necessarily have independent increments. Existence, uniqueness, regularity and large time behaviour will be treated and the general results will be applied to fractional noises or the Rosenblatt process. 2. Qualitative properties and numerical schemes for nonlinear SPDEs, for example, equations with jumps, reaction-diffusion equations and Navier-Stokes equations, nonlinear wave equations on flat spaces and Riemannian manifolds. 3. Optimal control of non- Markovian systems described in item 1) . 4. Brownian web and its relations to stochastic flows.