I don't know much about quantum linear response theory but I am also trying to learn. I found a series of lecture notes by Andrei Tokmakof at MIT. This one seems to be the most relevant.
http://www.mit.edu/~tokmakof/TDQMS/Notes/8._Linear_Response_2-09.pdf.
There are two books referenced on page 20 of the notes linked to in post #2. In the book by Mazenko, section 2.1 is useful. You may also want to check the 4th chapter of Kubo's et al. book <Statistical Physics II>.
It is worth noting that this theory is very "practical", in that it allows you to figure out what you would actually MEASURE in an experiment on a quantum system.
Years ago I e.g. used it to calculate the impedance(in ohms) of a driven system (described by a JC hamiltonian) as a function of applied magnetic field, which in turn allowed me to model a particular experiment to see if it was feasible.
Very useful.