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I'm totally ignorant about the Universal Coefficient Spectral Sequence (I used to work only with principal ideal domains, where the Universal Coefficient Theorem only amounts to a short exact sequence) but I need now to understand it. The book I was redirected to is the infamous User's Guide to SS where I have only been able to find very general versions (one about spectra and the other with functors on general abelian categories). I guess that an exposition in the simple case of chain complexes of A-modules exists somewhere, but I don't know where to look.

Do you have any suggestion?

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    *What* universal coefficient theorem? A very general theorem which you can use to obtain such results in the hypertor spectral sequence, which you can find explained in Wiebel, or McCleary, among others.2011-02-04
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    http://mathoverflow.net/questions/165714/kunneth-spectral-sequence has a reference to Rotman. Künneth theorems are generalizations of universal coefficient ones.2015-11-26
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    Essentially, theorem 10.90 in Rotman's Intro to homological algebra, second edition.2015-11-26

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