Gravity waves in the atmosphere are the waves with gravity and buoyancy force as the restoring forces. Gravity waves will significantly impact the Mesosphere Lower / Thermosphere (MLT), and the breaking of gravity waves is the key factor to cause the cool summer and warm winter in the Mesopause region. Therefore, it is important for us to investigate gravity waves. In this dissertation, we mainly use USU Na lidar data to explore gravity waves in the MLT. The exploration is made up of two projects. One is the investigation of gravity wave breaking and the associated dynamic instability by USU Na Lidar and Advanced Mesosphere Temperature Mapper (AMTM). Another is the calculation of gravity wave temperature perturbations and potential energy density by least-squares fitting based on the data from the full-diurnal cycle observation of Na lidar. The sporadic sodium layer is the sharp increase of Na density in a small vertical range (several kilometers) above the Na main layer in the MLT. The formation of the sporadic sodium layer above 100 km remains unknown until now. Here we will investigate the mechanism of the generation of sporadic sodium layer using numeric modeling, including the effect of tide and gravity wave on the variation of Na density.