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I've heard about many kinds of logic like combinatory logic, relevance logic, higher order logic, paraconsistent logic... but I don't know anything about those logical system except higher order logic.

Is there an overview or meta-tutorials about all logical systems? In particular, I'd like to know why those logic system are made and what their applications are.

How to classify them?

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The "Handbook of Philosophical Logic" by Gabbay et al. (several volumes) is a very nice source to get into a specific non-classical logic (the volumes are divided in surey articles of several non-classical logics). For a short introduction of the landscape of non-classical logics, I recommend Priest's book. –  Charlie Dec 25 '11 at 19:48

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Perhaps the best overview from a mathematicial perspective is Graham Priest's An Introduction To Non-Classical Logic. The second edition is much more detailed, and if you only want a survey, you may prefer the first edition, if you can find it.

Susan Haack's Philosophy of Logics is more philosophical, but still good for an overall impression of the subject.

Another excellent, and more recent book on the subject is Philosophical Logic, by John Burgess. All three of these books are written by philosophical logicians, perhaps because the motivation for studying non-classical logics often arises from philosophical concerns.

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thanks. is there a pdf or online version? I can't afford this now –  snowcake and icejelly Dec 25 '11 at 23:52
    
Not that I'm aware of, but the many articles on varient logics at the Stanford Encylopedia of Philosophy are excellent. –  antirealist Dec 26 '11 at 12:51
    
@snowcake and icejelly: For an introductory treatment, you may want to look at Eric Schechter's book Classical and Nonclassical Logics (2005). math.vanderbilt.edu/~schectex/logics –  Dave L. Renfro Dec 27 '11 at 15:01
    
@snowcake: Take a look at mathoverflow.net/questions/2147/… There you can find one of "the most useful math resources from the web" –  boumol Dec 30 '11 at 11:05

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