  We present enumerative aspects of the Gross-Siebert program in this
introductory survey. After sketching the program's main themes and goals, we
review the basic definitions and results of logarithmic and tropical geometry.
We give examples and a proof for counting algebraic curves via tropical curves.
To illustrate an application of tropical geometry and the Gross-Siebert program
to mirror symmetry, we discuss the mirror symmetry of the projective plane.
