  We describe, up to degree equal to the rank, the Lie algebra associated with
the automorphism group of a free group. We compute in particular the ranks of
its homogeneous components, and their structure as modules over the linear
group.
  Along the way, we infirm (but confirm a weaker form of) a conjecture by
Andreadakis, and answer a question by Bryant-Gupta-Levin-Mochizuki.
