Bizarrely, most of the expositions of Lyapunov stability theory--in particular his second method--I only know of engineering or applied references to. I'd love to get my hands on something which discusses it with the same level of rigor that say, Rudin delivers for his analysis books, Greub his linear Algebra book, etc.
I'd be looking first and foremost for a full published book (or review article), rather than an informal set of notes or slides posted online.
Leads, anyone?