  We calculate the automorphism group of a complete toric variety $X$ with
torus $T_M$. We prove that the radical unipotent of $Aut_k^0X$ is a semidirect
product of additive groups, the reductive part is a quotient of a product of
lineal groups and we give the action of linear groups on the additive groups.
We also prove that $Aut_kX/Aut_k^0X$ is a quotient of the group of
automorphisms of $M$ leaving invariant the fan.
