  The paper establishes a formula for enumeration of curves of arbitrary genus
in toric surfaces. It turns out that such curves can be counted by means of
certain lattice paths in the Newton polygon. The formula was announced earlier
in http://arxiv.org/abs/math.AG/0209253.
  The result is established with the help of the so-called tropical algebraic
geometry. This geometry allows one to replace complex toric varieties with the
Euclidean n-space and holomorphic curves with certain piecewise-linear graphs
there.
