The popularity of small unmanned aerial vehicles (UAVs) is increasing. Therefore, the importance of security systems able to detect and classify them is increasing as well. In this paper, we propose a new approach for UAVs classification using continuous wave radar or high pulse repetition frequency (PRF) pulse radars. We consider all steps of processing required to make a decision out of the raw radar data. Before the classification, the micro-Doppler signature is filtered and aligned to compensate the Doppler shift caused by the target's body motion. Then, classification features are extracted from the micro-Doppler signature in order to represent information about class at a lower dimension space. Eigenpairs extracted from the correlation matrix of the signature are used as informative features for classification. The proposed approach is verified on real radar measurements collected with X-band radar. Planes, quadrocopter, helicopters, and stationary rotors as well as birds are considered for classification. Moreover, a possibility of distinguishing different number of rotors is considered. The obtained results show the effectiveness of the proposed approach. It provides the capability of correct classification with a probability of around 92%.