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

Extended BRST symmetries. Quantum approach