Below is a list of the most important changes to the notes, together with known issues:

• Lecture 1:


• Lecture 2:
  30/3/2008: Corrected the proof that a reductive group is unramified almost everywhere (up to a statement which I haven't checked carefully, any references?).
  15/3/2012: The claim on top of page 4, that H^1(Inn G) injects into H^1(Aut G) is wrong: different elements of H^1(Inn G) can give rise to isomorphic inner forms.
  15/3/2012: I've been meaning to edit this ever since Brian Conrad pointed it out to me four years ago, and still didn't get around to it! The "real" reason why a globally defined connected reductive group is unramified almost everywhere is the existence of a reductive model with connected geometric fibers over the S-integers (for some finite set of places S) together with the existence of a smooth scheme parametrizing Borel subgroups.
  


• Lecture 2 1/2:
  24/12/2007: Added a paragraph on the Hasse principle.
  24/12/2007: I corrected the statement about the group structure on H¹(G): It comes from the group structure of the cohomology of a maximal anisotropic torus, not any torus.


• Lecture 3:
  20/12/2007: Added a paragraph on the Chebotarev density theorem.


• Lecture 4:
  19/2/2008: Added a paragraph on Tamagawa measures.
  30/3/2008: Strong approximation for simple groups, or otherwise we have to require that no factor is compact in $\Sigma$.


• Lecture 5:
  


• Lecture 6:
  


• Lecture 7:
  30/3/2008: The relative Weyl group is N(S)/Z(S), not N(S)/S.
  30/3/2008: The Satake isomorphism is canonical, not up to constant.

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