  The LO hadronic vacuum polarization (VP) contribution to the muon anomalous
magnetic moment $a_\mu$ is obtained as the integral as a function of energy of
an expression that involves the ratio of the $e^+e^- \rightarrow
\mathrm{hadron}$ cross section to the pointlike muon pair cross section. The
former is extracted from experimental data for individual hadronic final states
at low energies, and from perturbative QCD at high energies. The BaBar
experiment at SLAC has a programme of systematic measurement of the production
of the lowest-rest-mass hadronic final states, those that contribute most
significantly to the integral. To that purpose, we use a method in which, while
the PEP-II storage ring is operated at a constant energy in the center of mass
system, $\sqrt{s}$, of about 10.6 GeV, events are reconstructed and selected
which have been produced with a hadronic final state together with a
high-energy photon which may (photon tagging) or may not (no tagging) be
observed. In our kinematic configuration the photon is almost always emitted by
the electron or by the positron of the initial state, hence the name
"initial-state radiation" (ISR). The cross section for the direct $e^+e^-
\rightarrow f$ production of a final state $f$ at an energy $\sqrt{s'}$ is then
extracted from the differential cross section of the ISR production of the
state $f$ with invariant mass $\sqrt{s'}$. The programme is almost completed
and has lead to a number of first measurements and to an improvement of up to a
factor of three of the uncertainties on the contributions of individual
channels to $a_\mu$.
