Extended BRST symmetries. Quantum approach

The aim of this lecture is to present in a comprehensible way what the BRST quantization means and how the "classical" master equation, action and BRST transformations have to be prolonged towards the same "quantum" items. The presentation will focus not only on the standard BRST symmetry, but on larger symmetries as sp(2), both in the Lagrangean and in the Hamiltonian formalisms. How to find answers to these questions in more sophisticated cases will be illustrated by the example of a nonlinear system with open superalgebra.