  We study the representations of the quantum Galilei group by a suitable
generalization of the Kirillov method on spaces of non commutative functions.
On these spaces we determine a quasi-invariant measure with respect to the
action of the quantum group by which we discuss unitary and irreducible
representations. The latter are equivalent to representations on \ell^2, i.e.
on the space of square summable functions on a one dimensional lattice.
