  In 1967 Moser proved the existence of a normal form for real analytic
perturbations of vector fields possessing a reducible Diophantine invariant
quasi-periodic torus. In this paper we present a proof of existence of this
normal form based on an abstract inverse function theorem in analytic class.
The given geometrization of the proof can be opportunely adapted accordingly to
the specificity of systems under study. In this more conceptual frame, it
becomes natural to show the existence of new remarkable normal forms, and
provide several translated-torus theorems or twisted-torus theorems for systems
issued from dissipative generalizations of Hamiltonian Mechanics, thus
providing generalizations of celebrated theorems of Herman and R\"ussmann, with
applications to Celestial Mechanics.
