TITLE: Looking for a mathematically rigorous introduction to game theory
QUESTION [23 upvotes]: I am looking for the best book that contains a mathematically rigorous introduction to game theory.  
I am a group theorist who has taken a recent interest in game theory, but I'm not sure of the best place to learn about game theory from first principles.  Any suggestions?  Thanks!

REPLY [3 votes]: An Introductory Course on Mathematical Game Theory by González-Díaz, García-Jurado and Fiestras-Janeiro
Reviews can be found here: 1, 2, 3.
Taken from the second review:

The book is self-contained and written very
  rigorously, but on the other hand, it is also very friendly to the reader, containing a lot of explanations
  and interpretations of game theory notions, as well as very many examples describing and
  analyzing various economic and other models with an application to game theory results. This
  makes it very suitable for graduate and advanced undergraduate courses on game theory.