Atmospheric Neutrino Physics with the MACRO detector

We present the measurement of the the flux and angular distribution of atmospheric muon neutrinos using the MACRO detector. Three different event topologies are detected in two different energy ranges. High energy neutrinos (E~80 GeV) via the identification of upward throughgoing muons. Lower energy neutrinos (E~ 4 GeV) via the upgoing stopping and partially contained downgoing muons (ID+UGS), or via the partially contained upgoing muons (IU). The measured flux is reduced with respect to the predictions. For the high energy sample, globally the flux reduction is $0.74\pm 0.054_{stat+sys} \pm 0.12_{th}$ and varies with the zenith angle. The ratio of measured to expected events is almost constant with the zenith angle for the low energy events, and is $0.57 \pm 0.08_{stat+sys} \pm 0.14_{theor}$ for the IU sample, and $0.71 \pm 0.09_{stat+sys} \pm 0.17_{theor}$ for the (ID+UGS). All the data sets are consistent within a scenario of neutrino oscillations, with maximum mixing and $\Delta m^2 \sim 10^{-3}\div 10^{-2} eV^2$.