  Starting from Wigner's symmetry representation theorem, we give a general
account of discrete symmetries (parity P, charge conjugation C, time-reversal
T), focusing on fermions in Quantum Field Theory. We provide the rules of
transformation of Weyl spinors, both at the classical level (grassmanian wave
functions) and quantum level (operators). Making use of Wightman's definition
of invariance, we outline ambiguities linked to the notion of classical
fermionic Lagrangian. We then present the general constraints cast by these
transformations and their products on the propagator of the simplest among
coupled fermionic system, the one made with one fermion and its antifermion.
Last, we put in correspondence the propagation of C eigenstates (Majorana
fermions) and the criteria cast on their propagator by C and CP invariance.
