In underlay cognitive radio networks, secondary users can share the spectrum with primary users as long as the interference caused by the secondary users to primary users is below a certain predetermined threshold. It is reasonable to assume that there is always a large pool of secondary users trying to access the channel, which can be occupied by only one secondary user at a given time. As a result, a multi-user scheduling problem arises among the secondary users. In this thesis, by manipulating basic schemes based on selective multi-user diversity, normalized thresholding, transmission power control, and opportunistic round robin, we propose and analyze eight scheduling schemes of secondary users in an underlay cognitive radio set-up. The system performance of these schemes is quantified by using various performance metrics such as the average system capacity, normalized average feedback load, scheduling outage probability, and system fairness of access. In our proposed schemes, the best user out of all the secondary users in the system is picked to transmit at each given time slot in order to maximize the average system capacity. Two thresholds are used in the two rounds of the selection process to determine the best user. The first threshold is raised by the power constraint from the primary user. The second threshold, which can be adjusted by us, is introduced to reduce the feedback load. The overall system performance is therefore dependent on the choice of these two thresholds and the number of users in the system given the channel conditions for all the users. In this thesis, by deriving analytical formulas and presenting numerical examples, we try to provide insights of the relationship between the performance metrics and the involved parameters including two selection thresholds and the number of active users in the system, in an effort to maximize the average system capacity as well as satisfy the requirements of scheduling outage probability and feedback load.