  Based on the large N duality relating topological string theory on Calabi-Yau
3-folds and Chern-Simons theory on 3-manifolds, M. Aganagic, A. Klemm, M.
Marino and C. Vafa proposed the topological vertex (hep-th/0305132), an
algorithm on computing Gromov-Witten invariants in all genera of any
non-singular toric Calabi-Yau 3-fold. In this expository article, we describe
the mathematical theory of the topological vertex developed by J. Li, K. Liu,
J. Zhou, and the author (math/0408426).
