  A Lie system is a system of differential equations describing the integral
curves of a $t$-dependent vector field taking values in a finite-dimensional
real Lie algebra of vector fields, a Vessiot-Guldberg Lie algebra. We define
and analyze Lie systems possessing a Vessiot-Guldberg Lie algebra of
Hamiltonian vector fields relative to a Jacobi manifold, the hereafter called
Jacobi-Lie systems. We classify Jacobi-Lie systems on $\mathbb{R}$ and
$\mathbb{R}^2$. Our results shall be illustrated through examples of physical
and mathematical interest.
