The analysis on manifolds with singular geometry (such as conical points,edges,corners,higher polyhedral singularities) gives rise to a new machinerie of operators with symbolic structures which is able to express parametrices and the regularity of solutions to boundary value problems of elliptic equations.Simplest examples are mixed problems of Zaremba type,crack problems,or situations when potentials in the operators have singularities at special points or along interfaces within the domain (for instance,Coulomb or other potentials in Schroedinger operators,coming from the position of particles).