ttbar and single top cross sections at the Tevatron

We present a summary of the latest measurements of the top pair and single top cross sections performed by the CDF and D0 collaborations at the Fermilab Tevatron collider. The Fermilab Tevatron collider ended its run on September 30, 2011 after delivering more than 10 fb{sup -1} of p{bar p} collision data per experiment at {radical}s = 1.96 TeV. A large sample of top quarks collected by the CDF and D0 experiments allows to perform precision measurements of their production which is predicted to occur within the standard model (SM) either in pairs via strong interactions or as single top events via electroweak interactions. Such measurements represent an important test of the theoretical calculations which predict the t{bar t} and single top production cross sections with a precision of 6% to 8% and 5%, respectively. Precise measurements of top pair cross section ({sigma}{sub t{bar t}}) in different t{bar t} final states and single top production via different production mechanisms are highly desirable as they are sensitive to the non-SM particles that may appear in top quark production or decays.