We describe, up to degree n, the Lie algebra associated with the automorphism group of a free group of rank n. 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.