  Tropical algebraic geometry is the geometry of the tropical semiring
$(\mathbb{R},\min,+)$. Its objects are polyhedral cell complexes which behave
like complex algebraic varieties. We give an introduction to this theory, with
an emphasis on plane curves and linear spaces. New results include a complete
description of the families of quadrics through four points in the tropical
projective plane and a counterexample to the incidence version of Pappus'
Theorem.
