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Not exactly an "online course", but these notes (used for an undergrad course on games) I found quite readable: http://math.ucr.edu/home/baez/games/

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I can recommend the book 'A Course in Game Theory' by Ariel Rubinstein and Martin J. Osborne . You'll probably need some mathematical and economic background knowledge to gain the most out of it. Note that it is more abstract than illustrative though it is aimed at a beginner in Game Theory.

The book ist free to download after a simple registration at http://arielrubinstein.tau.ac.il/books.html

That's a good book, but a bit advanced. A little bit easier is Osborne's Introduction to Game Theory.

On the heavier side, Game Theory by Tirole and Fudenberg is used in a lot of graduate economics programs.

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