A semialgebraic set is a subset S of R^n defined by a finite sequence of polynomial equations P=0 and inequalities Q > 0, or any finite union of such sets. In this talk, I will introduce some basic properties of semialgebraic sets, including that they are closed under the projection operation and triangularizable. If time permits, I will show an explicit bound for the number of connected components of a real algebraic set as a function of the degree of the equations and the dimension of the ambient space.