In [PR1, Chap. VIII], we described the free completely simple semigroup. In the first few sections of [PR2, Chap. 1 ], we described the Clifford model of the free completely regular semigroup and gathered the basic information regarding the structure of the free completely regular semigroup as well as its fully invariant congruences. When dealing with any variety, the first objects of interest are often the free objects, since they are the most general and any information that we can obtain about them has a strong influence on what we can discover regarding its members and subvarieties.