<p>Atmospheric escape rate is a key parameter to measure in order to understand the evolution of exoplanets. In this presentation, we will show that the Balmer series, observed with high-resolution transmission spectroscopy, is a precise probe to measure exoplanet evaporation, especially for ultra hot Jupiters orbiting early-type star. These&#160;hot gaseous giant exoplanets (such as KELT-9 b) are presumed to have an atmosphere dominated by neutral and ionized atomic species. In particular, hydrogen Balmer&#160;lines have been detected in some of their upper atmospheres, suggesting that hydrogen is filling the planetary Roche lobe and escaping&#160;from these planets. Here, we will present new significant absorptions of the Balmer series in the KELT-9b atmosphere obtained with HARPS-N. The precise line shapes of the H&#945;,&#160;H&#946;, and H&#947; absorptions allow us to put constraints on the thermospheric temperature. Moreover, the mass loss rate, and the excited&#160;hydrogen population of KELT-9 b are also constrained, thanks to a retrieval analysis performed with a new atmospheric model (the PAWN model). We&#160;retrieved a thermospheric temperature of T = 13 200+800-720 K and a mass loss rate of log10(MLR) = 10^(12.8+-0.3) g/s when the atmosphere was&#160;assumed to be in hydrodynamical expansion and in local thermodynamic equilibrium (LTE). Since the thermospheres of hot Jupiters&#160;are not expected to be in LTE, we explored atmospheric structures with non-Boltzmann equilibrium for the population of the excited&#160;hydrogen. We do not find strong statistical evidence in favor of a departure from LTE. However, our non-LTE scenario suggests that a&#160;departure from the Boltzmann equilibrium may not be sufficient to explain the retrieved low number densities of the excited hydrogen.&#160;In non-LTE, Saha equilibrium departure via photo-ionization, is also likely to be necessary to explain the data.</p>