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reference for (co)homology theories

Hi everyone,

Every now and then, I find myself dealing with such or such (co)homology theory, and I'm frustrated I don't feel more comfortable around it.

I was wondering if someone could recommend a cool reference that would, ideally:

  1. Cover several cohomology theories, including, say: singular, de Rham, Dolbeault, group cohomology, sheaf cohomology.
  2. Explain the relations between these theories.
  3. Not too hardcore to read (not too formal, containing examples, etc.)

Thanks for helping!