Tropical geometry is an exciting new field at the interface between algebraic geometry and combinatorics with connections to many other fields. At its heart it is geometry over the tropical semiring, which is R∪ with the usual operations of addition and multiplication replaced by minimum and addition respectively. This turns polynomials into piecewise linear functions,and replaces an algebraic variety by an object from polyhedral geometry,which can be regarded as a “combinatorial shadow” of the original variety.