We discuss the final results of the MACRO experiment on atmospheric neutrino oscillations .
The data concern event topologies with average neutrino energies of \sim 3 and \sim 50 GeV .
Multiple Coulomb Scattering of the high energy muons was used to estimate the neutrino energy event by event .
The angular distributions , the L / E _ { \nu } distribution , the particle ratios and the absolute fluxes all favor \nu _ { \mu } \rightarrow \nu _ { \tau } oscillations with maximal mixing and \Delta m ^ { 2 } \simeq 0.0023 \ > eV ^ { 2 } .
Emphasis is given to measured ratios which are not affected by Monte Carlo ( MC ) absolute normalization ; a discussion is made on MC uncertainties .
A preliminary search for possible Lorentz invariance violation contributions to atmospheric neutrino oscillations is presented and discussed .