I don't understand what's the meaning of "cited after" in books, when they cite a source, e.g.,

(cited after Manin 1997: 3)


It means that the author didn't actually look the quote up himself (didn't actually read the source cited in "The Principles of Representative Government", in this case) but instead relied on another author to come up with the correct citation. It's a second-hand quote, if you will, and usually a no-go in serious academic writing (except, perhaps, in somy very exceptional circumstances, if you've cleared it with your academic advisor.)