The Recycler Electron Cooler (REC) was the first cooler working at a relativistic energy (gamma = 9.5). It was successfully developed in 1995-2004 and was in operation at Fermilab in 2005-2011, providing cooling of antiprotons in the Recycler ring. After introducing the physics of electron cooling and the REC system, this paper describes measurements carried out to tune the electron beam and optimize its cooling properties. In particular, we discuss the cooling strategy adopted for maximizing the collider integrated luminosity.