Grothendieck in his Esquisse d'un programme mentioned without any precise definition and construction that the absolute Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$ acts on the whole "tower" of the Teichmuller groupoids $\hat T_{g,\nu}$ (see p.5 in the above reference).

I do understand what does that mean in a very special case $g=0,\nu=4$.

What does it mean in general? What are these Teichmuller groupoids? Is there a more detailed exposition of the above general remark of Grothendieck?

ADD: If I understand correctly, $\hat T_{g,\nu}$ is very close to be a profinite completion of the fundamental group of the moduli space $M_{g,\nu}$ of smooth Riemann surfaces of genus $g$ with $\nu$ marked points (am I wrong?). Grothendieck claims that there are various natural morphisms between $\hat T_{g,\nu}$'s. Frankly I do not see any morphisms except $\hat T_{g,\nu}\to \hat T_{g,\mu}$ for $\mu<\nu$ induced by the map $M_{g,\nu}\to M_{g,\mu}$ which is just forgetting several marked points. Are there any other morphisms?