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I've been trying to learn about algebraic groups lately and I was wondering if there were any books/notes out there which: A. treat algebraic groups over the complex numbers, B. cover all the most frequently encountered buzzwords (reductive, semisimple, borel, levi, cartan, weyl, weights, roots...), C. have many worked out examples.

I only know of Fulton-Harris and Onischik-Vinberg, but I was wondering if there others out there (for whatever reason, I find both a tough read).

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    $\begingroup$ The point with algebraic groups is precisely that the theory (including all that concerns your buzzwords) is the same for all algebraically closed fields of characteristic zero....! Take Springer or Borel (or any other) and replace the field with the complex field, if you feel more comfortable. $\endgroup$
    – YCor
    Sep 27, 2017 at 14:33
  • $\begingroup$ @YCor but which of those books would you recommend? $\endgroup$
    – Yosemite Sam
    Sep 27, 2017 at 18:24
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    $\begingroup$ I strongly disagree with closing this question as a "duplicate". First of all, the OP asked for references which specifically treat algebraic groups in characteristic zero which is not at all the same as elementary. In characteristic zero one can do things one cannot even dream of in positive characteristic (complete reducibility, slice theorem etc.) Secondly, the purported duplicate is 7 years old and there do exist new books on the market, like Goodman-Wallach. I vote to reopen. $\endgroup$
    – Friedrich Knop
    Sep 27, 2017 at 19:58
  • $\begingroup$ @FriedrichKnop you can still contribute to the older question to mention recent books $\endgroup$
    – YCor
    Sep 28, 2017 at 1:10

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