These are the notes for my series of lectures in the mini-cours in Lens, France, in June 2006. They have three parts.

1. The first part contains material that was developed for inclusion in Serre's portion of the book Cohomological invariants in Galois cohomology, but was eventually not included. That part culminates with the determination of the mod p invariants of PGL_p and the mod 3 invariants of Albert algebras. I learned most of this material from Serre.
2. The second part is harder to describe. Briefly, it proves certain surjections in Galois cohomology. It also discusses the mod 3 invariants of groups of type E₆ and E₇ and the mod 5 invariants of groups of type E₈.
3. The third part gives a detailed account of Markus Rost's results on cohomological invariants and essential dimensions of Spin_n for n at most 14. His original notes can be found on his webpage.