TITLE: What is Eisenstein series?
QUESTION [13 upvotes]: There are several related questions here, the latter being especially interesting. We know the classical Eisenstein series.

What are the Eisenstein series on a group G and why they are interesting?
What's the geometric analogue of Eisenstein series? I think I saw the definition, but what's its importance?

REPLY [4 votes]: I highly recommend Drinfeld's lectures on Eisenstein series, notes available at
http://www.math.utexas.edu/users/benzvi/GRASP/lectures/drinfeldEisen.pdf