We give an introduction to Tropical Geometry and prove some results in
Tropical Intersection Theory. The first part of this paper is an introduction
to tropical geometry aimed at researchers in Algebraic Geometry from the point
of view of degenerations of varieties using projective not-necessarily-normal
toric varieties. The second part is a foundational account of tropical
intersection theory with proofs of some new theorems relating it to classical
intersection theory.

Revised version includes corrections and new proofs relating on lattice
indices and the associated cycle.