  It is demonstrated that strong magnetic fields are produced from a zero
initial magnetic field during the pregalactic era, when galaxies are first
forming. Their development proceeds in three phases. In the first phase, weak
magnetic fields are created by the Biermann battery mechanism, acting in
shocked parts of the intergalactic medium where caustics form and intersect. In
the second phase, these weak magnetic fields are amplified to strong magnetic
fields by the Kolmogoroff turbulence endemic to gravitational structure
formation of galaxies. During this second phase, the magnetic fields reach
saturation with the turbulent power, but they are coherent only on the scale of
the smallest eddy. In the third phase, the magnetic field strength increases to
equipartition with the turbulent energy, and the coherence length of the
magnetic fields increases to the scale of the largest turbulent eddy,
comparable to the scale of the entire galaxy. The resulting magnetic field
represents a galactic magnetic field of primordial origin. No further dynamo
action is necessary, after the galaxy forms, to explain the origin of magnetic
fields. However, the magnetic field may be altered by dynamo action once the
galaxy and the galactic disk have formed. It is first shown by direct numerical
simulations, that thermoelectric currentsassociated with the Biermann battery,
build the field up from zero to $10^{-21}$ G in the regions about to collapse
into galaxies, by $z\sim3$. For weak fields, in the absence of dissipation, the
cyclotron frequency ${\bf \omega_{cyc}}=e{\bf B } /m_H c $ and $ {\bf
\omega}/(1+ \chi )$, where ${\bf \omega = \nabla \times v }$ is the vorticity
and $\chi$ is the degree of ionization, satisfy the same equations, and initial
conditions ${\bf \omega_{cyc}=\omega}=0$, so that, ${\bf \omega_{cyc}}({\bf
