This article presents a neural network-based approach to classify UAVs or drones from range-doppler and micro-doppler radar signatures. Training datasets for six drone types that have captured rotor blade rotation speed and drone dynamic motion behavior in a number of scenarios are considered including environments with multiple drones. A 77 GHz FMCW radar is used to generate datasets. Blade radial velocities up to 50 m/s, drone velocities up to 10 m/s and range distances up to 60 meters are considered in the datasets. A classification accuracy greater than 97% was achieved with this technique. Potential applications include agriculture, ecosystem management, first responder disaster assessment, cinematography, safety, security and many others.