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I'm not sure if this is the right place (or physics.stackexchange?) to ask the next

  1. What is the difference between fuchsian, theta-fuchsian, and kleinian functions?

  2. Please, suggest me an introductory reference to the Physics of previously asked for.

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Do you mean Fuchsian and Kleinian groups? (These are discrete subgroups of $PSL(2;\mathbb{R})$ and $PSL(2;\mathbb{C})$, respectively.) – Neal Nov 26 '12 at 16:56
That's right, but in other words I'm looking for examples of use in Physics. – paritto Nov 27 '12 at 0:54
If that's your chief question, I guess you might get a better response at physics.SE. – Neal Nov 27 '12 at 3:27

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