Book about different kinds of logic. I'm searching for a book that talks about different kinds of logic (esoteric and particular ones too) and their uses and differences.
Does such a book exist?

If by esoteric and particular you mean that the book is based solely on a single non-classical logic, then here are some examples:
Fuzzy Equational Logic (Belohlavek, Vychodil), 
Modal Logic (Blackburn)
If you want something that simply exposits many different non-classical logics and says a little bit more about non-classical logics in general, there's "An Introduction to Non-classical Logic - From If to Is" by Priest.
