I highly recommend reading Edward Frenkel's memoir, Love and Math, which is more or less an up close and personal popular account of the author's involvement with the Langlands Program:
Perhaps the most remarkable part of the book though is the way it makes a serious attempt to tackle the problem of explaining one of the deepest sets of ideas in mathematics, those which go under the name of the “Langlands program”. These ideas have fascinated me for years, and much of what I have learned about them has come from reading some of Frenkel’s great expository articles on the subject. To anyone who wants to learn more about this subject, the best advice for how to proceed is to read the overview in “Love and Math” (which you likely won’t fully understand, but which will give you a general picture and glimpses of what is really going on), and then try reading some of his more technical surveys [...]
http://www.math.columbia.edu/~woit/wordpress/?p=6266
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