Absolute Galois groups - old and new results

Galois theory investigates the symmetry patterns among roots of polynomials over a field. These symmetry patterns are described by the absolute Galois group of the field, whose structure is in general still a mystery. We will describe what is known about this symmetry group: classical facts, consequences of the epochal work by Veovodsky and Rost, and very recent structural results and conjectures related to higher cohomology operations and intersection theorems.