Cognitive radio is an efficient approach to access frequency spectrum. The performance of cognitive radio networks is substantially determined by the information on spectrum occupancies. Experiments have demonstrated the temporal and spatial correlations of spectrum availability, which is of key importance in the design and analysis of cognitive radio networks. Motivated by the observation, this research studies the social interaction mechanism for secondary users to fully exploit the correlations. A recommendation mechanism is useful for secondary users to share correlated information about the spectrum. Collaborative filtering can enhance the capability of better learning the spectrum situations. For better understand and assist the design, analysis is conducted for the social interaction mechanism, based on powerful tools in social networks, such as master equation, mean filed dynamics and epidemic propagation. Continuum model, such as partial differential equations for diffusions, is also employed as the limit case of discrete cognitive radio networks. Beacon based and packet based mechanisms are used for the recommendation protocols. A 100-node hardware cognitive radio network testbed is built to demonstrate the proposed mechanisms, algorithms and protocols. The research involves aspects of wireless communications, networking, artificial intelligence and physics; thus the inter-disciplinary essence of the research also lends itself to cross-disciplinary education. New courses are devised, which involve the topics of cognitive radio networks, machine learning and image processing. This project also attracts traditionally underrepresented groups, as well as outreach high school students.