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Where can I find some reference about integrability of vector fields and Frobenius's theorem?

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Boothby is a nice easy to read reference for this. – David Carchedi Jun 8 2010 at 11:45
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 As it stands, this question could do with some improvement. There are plenty of standard texts on this so what is wrong with those? What level are you looking for? What do you already know? – Andrew Stacey Jun 8 2010 at 11:57
There are three or four different proves of the Frobenius' theorem. They are all quite similar in character. The one I think is the clearest and most to the point is presented in the book "Geometric Theory of Foliations" by Camacho and Cesar. Unfortunately, google books doesn't display the relevant section. books.google.com/…'%20theorem&f=false If you can't get the book, you can find its proof here ams.org/mathscinet/search/… – James O Jun 8 2010 at 14:24
The link to the ams review above doesn't seem to work. Here is the paper jstor.org/stable/2159499?seq=1 The proof presented here, in my opinion, is almost as good as the one in Geom. Foliation Theory. Unfortunately, it may be hard to get hold of a copy of Geom. Foliation Theory. It is the best introduction to integrable distributions that I know of. – James O Jun 8 2010 at 14:38

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