Finite field models in additive combinatorics

The study of many problems in additive combinatorics, such as Szemer\'edi's
theorem on arithmetic progressions, is made easier by first studying models for
the problem in F_p^n for some fixed small prime p. We give a number of examples
of finite field models of this type, which allows us to introduce some of the
central ideas in additive combinatorics relatively cleanly. We also give an
indication of how the intuition gained from the study of finite field models
can be helpful for addressing the original questions.