I've been trying to find an extensive, in-depth treatment of rational zeta series. Via the Wikipedia article on the topic, I've found two articles on this subject. While they are certainly very informative, I wonder whether there is a more comprehensive treatment that -- among perhaps other things -- provides an introduction on the summation methods, summarizes all the known results to date, shows what the open problems in the domain are, and shows how the summation of zeta terms relates to finding the sum of terms of other (Dirichlet) series.
I've asked a related question on MSE. The question above is a slightly modified and somewhat more elaborate version of it.