  In 1976, Appel and Haken achieved a major break through by proving the four
color theorem $(4CT)$. Their proof is based on studying a large number of cases
for which a computer-assisted search for hours is required. In 1997, Robertson,
Sanders, Seymour and Thomas reproved the 4CT with less need for computer
verification. In this paper, we present a simple proof to the $4CT$ based on
mathematical induction and contraction. We consider, in our proof, possible
colorings of a minimum degree vertex, its adjacent vertices and adjacent
vertices of these adjacent vertices of simple planar graphs.
