Books:
- The standard reference on Algorithmic Game Theory is the book by Nisan, Tardos, Roughgarden, and Vazirani.
Algorithmic Game Theory
http://www.cambridge.org/journals/nisan/downloads/Nisan_Non-printable.pdf
- Another book on AGT is by Kevin Leyton-Brown from UBC and Yoav Shoham from Stanford:
Multi-Agent Systems: Algorithmic, Game-Theoretic and Logical Foundations
A free electronic copy has been made available by the authors as well:
http://www.masfoundations.org/mas.pdf
I think there are half a dozen books by Roughgarden with "Twenty Lectures on Algorithmic Game Theory" being one of the best books for beginners. All Books are available on amazon.
Courses:
If you're interested in lecture notes and video lectures on Algorithmic Game Theory, then I would strongly urge you to have a look at Tim Roughgarden's course website:
Algorithmic Game Theory (CS364A), Fall 2013
His lectures are amazing and surprisingly easy to grasp, especially considering the theoretical nature of the subject matter.
There's also a sequel course on Mechanism Design if you're interested:
Frontiers in Mechanism Design (CS364B), Winter 2014
If you're looking to brush up on a few game theory fundamentals you could go through the following two courses offered by Coursera:
Introductory Course on Game Theory
https://www.coursera.org/course/gametheory
Advanced Applications of Game Theory: Auctions and Social Choice Theory
https://www.coursera.org/course/gametheory2