Tropical geometry is the geometry over the tropical semiring, which is the set of real numbers where the tropical addition is taking the minimum, and the tropical multiplication is the ordinary addition. As the ordinary linear and polynomial algebra give rise to convex geometry and algebraic geometry, tropical linear and polynomial algebra give rise to tropical convex geometry and tropical algebraic geometry. I will introduce these basic objects in tropical geometry and discuss their applications to other areas of pure and applied mathematics, such as enumerative geometry, computational algebra, and combinatorial optimization.