  We consider the energy critical four dimensional semi linear heat equation
\partial tu-\Deltau-u3 = 0. We show the existence of type II finite time blow
up solutions and give a sharp description of the corresponding singularity
formation. These solutions concentrate a universal bubble of energy in the
critical topology u(t,r)-1/{\lambda} Q(r/{\lambda})\rightarrow u* in
$\dot{H}^1$ where the blow up profile is given by the Talenti Aubin soliton
Q(r)= 1/(1 +r^2/8) and with speed {\lambda}(t) ~(T-t)/|log(T - t)|^2 as
t\rightarrowT. Our approach uses a robust energy method approach developped for
the study of geometrical dispersive problems, and lies in the continuation of
the study of the energy critical harmonic heat flow and the energy critical
four dimensional wave equation.
