A survey of the symmetric group for the working mathematician I

I will go over the combinatorics of partitions and symmetric functions and their relation to the representations of the symmetric group. Then I will explain the new point of view developed by Okounkov and Vershik. I will also cover other developments like the half-infinte wedge Fock space representation, and the methods available to deal with asymptotics of representation characters. I will focus especially on those methods inspired in statistical mechanics, such as the existence of limit shapes, and in their treatment using both variational calculus and stationary phase methods. I will also briefly talk about applications to some counting problems in algebraic geometry.