Given a fan , we associate to it a variety in the following way: we take the disjoint union of all affine toric varieties corresponding to the cones of the fan and then glue them together using the method: for any two cones \sigma and \tau in the fan, their intersection is a common face of both so that its corresponding toric affine variety is contained in both X_\sigma and X_tau as a principal open subvariety. Now glue X_{\sigma} and X_{\tau} along this common subvariety. The variety obatained in this way is called the toric variety associated with the fan. In the end I will talk about toric varieties associated to a polytope which turn out to be projective toric varieties.