If you have the time, I heartily recommend Ben Polak's Introduction to Game Theory lectures. They are highly watchable and give a very solid introduction to the topic.
In terms of books, The Strategy of Conflict is the classic popular work, and it's good, but it's very much a product of its time. I imagine there are more accessible books out there. Yvain recommends The Art of Strategy, which I haven't read.
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What are your motives for learning about it? If it's to gain a bare-bones understanding sufficient for following discussion in Less Wrong, existing Less Wrong articles would probably equip you well enough.
My possibly crazy theory is that game theory would be a good way to understand feminism.