*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 H^{1}(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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