  The BaBar Collaboration has an intensive program of studying hadronic cross
sections at low-energy $e^+e^-$ collisions, accessible via initial-state
radiation. Our measurements allow significant improvements in the precision of
the predicted value of the muon anomalous magnetic moment, that shed light on
the current $\approx$ 3.5 sigma difference between the predicted and the
experimental values. We have published results on a number of processes with
two to six hadrons in the final state. We report here the results of recent
studies with the final states that constitute the main contribution to the
hadronic cross section below 3 GeV, as $e^+e^- \rightarrow \pi^+\pi^-$,
$K^+K^-$, $K_S K_L$ and $e^+e^- \rightarrow 4$ hadrons.
