Context: Rapid rotation is a common feature of early-type stars but which remains a challenge for the models. The understanding of its effect on stellar evolution is however imperative to interpret the observed properties of numerous stars. Aims: We wish to bring more observational constraints on the properties of fast rotating stars, especially on their oscillation modes. Methods: We focus on the nearby star Altair which is known as a very rapidly rotating star with an equatorial velocity estimated recently at 313 km/s. We observed this star with the high-resolution spectropolarimeter Neo-Narval during six nights, with one night of interruption, in September 2020. Results: We detect significant line profile variations on the mean line profile of the spectra. Their time-frequency analysis shows that these variations are induced by gravito-inertial waves propagating at Altair's surface with azimuthal wavenumbers of order
. With a preliminary computation of the
eigenspectrum using the most recent concordance model of Altair we can give a
first modelling of the observed waves. Conclusions: Altair was known as the
brightest Scuti star. We now see that it is the brightest hybrid
oscillating star with excited gravito-inertial waves and acoustic waves.
Clearly, more observations and more advanced models are needed to explain the
observations in greater details