In addition to amhotw's suggestions (which are very good), I would recommend Myerson's book (https://www.amazon.co.uk/Game-Theory-Analysis-Roger-Myerson/dp/0674341163) if you want something a bit less terse than Osborne-Rubinstein. Even less terse - and perhaps even better at giving an intuitive feel for the various solution concepts - is the game theory part of Kreps's A course in Microeconomic Theory (https://www.amazon.co.uk/Course-Microeconomic-Theory-David-Kreps/dp/0691202753/).
I'm pretty sure a lot of the notation that is used today wasn't developed back then, so it might be worth your while to pick up a newer book. I would personally recommend Myersons text for a good introduction to game theory, but bear in mind it only really gives an introduction (it's pretty well priced though!).
Fudenberg and Tiroles text covers a few more topics, and I've still pulled out my copy of Von Neumann and Morgernsterns book occasionally to look things up, two that I can think of was a way for numerically approximating mixed strategy nash equilibria for 2 player zero sum games for an ai contest (I didn't end up doing it unfortunately) and for defining symmetric games.
Unfortunately, you will sometimes come across incorrect information as well, for example this definition for a symmetric game is incorrect, your condition needs to be either of the equivalent statemnts,
[; u_i(s_1, ..., s_n) = u_{\pi(i)} (s_{\pi^{-1}(1)}, ..., s_{\pi^{-1}(n)}) ;]
[; u_{\pi(i)}(s_1, ..., s_n) = u_i ( s_{\pi(1)}, ..., s_{\pi(n)} ) ;]
for all permutations of the players, pure strategies and players.
... and even this doesn't count games as symmetric if you permute players strategies.
edit: does anyone know why the latex isn't working?
Myersons book is great at covering the basic topics of game theory, Tirole and Fudenbergs book is slightly older and doesn't really explain some things as well, but it also covers a few more topics.
There's also a section on game theory in MWG, but I prefer the above texts just for game theory.