  A peculiarity of the geometry of the euclidean 3-sphere $\S3$ is that it
allows for the existence of compact without boundary minimally immersed
surfaces. Despite a wealthy of examples of such surfaces, the only known tori
minimally embedded in $\S3$ are the ones congruent to the Clifford torus. In
1970 Lawson conjectured that the Clifford torus is, up to congruences, the only
torus minimally embedded in $\S3$. We prove here Lawson conjecture to be true.
Two results are instrumental to this work, namely, a characterization of the
Clifford torus in terms of its first eingenfunctions (\cite{MR}) and the
assumption of a "two-piece property" to these tori: every equator divides a
torus minimally embedded in $\S3$ in exactly two connected components
(\cite{Rs}).
