  In the mid sixties, A. Grothendieck envisioned a vast generalization of
Galois theory to systems of polynomials in several variables, motivic Galois
theory, and introduced tannakian categories on this occasion. In characteristic
zero, various unconditional approaches were later proposed. The most precise
one, due to J. Ayoub, relies on Voevodsky theory of mixed motives and on a new
tannakian theory. It sheds new light on periods of algebraic varieties, and
shows in particular that polynomial relations between periods of a pencil of
algebraic varieties always arise from Stokes formula.
