  We present a constructive approach to torsion-free gradings of Lie algebras.
Our main result is the computation of a maximal grading. Given a Lie algebra,
using its maximal grading we enumerate all of its torsion-free gradings as well
as its positive gradings. As applications, we classify gradings in low
dimension, we consider the enumeration of Heintze groups, and we give methods
to find bounds for non-vanishing $\ell^{q,p}$ cohomology.
