Recently, there has been a massive growth in the number of mobile users and their traffic. The data traffic volume almost doubles every year. Mobile users are currently running multiple applications that require higher bandwidth which makes users so limited to the service providers' resources. Increasing the utilization of the existing spectrum can significantly improve network capacity, data rates and user experience. Spectrum sharing enables wireless systems to harvest under-utilized swathes of spectrum, which would vastly increase the efficiency of spectrum usage. Making more spectrum available can provide significant gain in mobile broadband capacity only if those resources can be aggregated efficiently with the existing commercial mobile system resources. Carrier aggregation (CA) is one of the most distinct features of 4G systems including Long Term Evolution Advanced (LTE-Advanced). In this dissertation, a resource allocation with carrier aggregation framework is proposed to allocate multiple carriers resources optimally among users with elastic and inelastic traffic in cellular networks. We use utility proportional fairness allocation policy, where the fairness among users is in utility percentage of the application running on the user equipment (UE). A resource allocation (RA) with CA is proposed to allocate single or multiple carriers resources optimally among users subscribing for mobile services. Each user is guaranteed a minimum quality of service (QoS) that varies based on the user's application type. In addition, a resource allocation with user discrimination framework is proposed to allocate single or multiple carriers resources among users running multiple applications. Furthermore, an application-aware resource block (RB) scheduling with CA is proposed to assign RBs of multiple component carriers to users' applications based on a utility proportional fairness scheduling policy. We believe that secure spectrum auctions can revolutionize the spectrum utilization of cellular networks and satisfy the ever increasing demand for resources. Therefore, a framework for multi-tier dynamic spectrum sharing system is proposed to provide an efficient sharing of spectrum with commercial wireless system providers (WSPs) with an emphasis on federal spectrum sharing. The proposed spectrum sharing system (SSS) provides an efficient usage of spectrum resources, manages intra-WSP and inter-WSP interference and provides essential level of security, privacy, and obfuscation to enable the most efficient and reliable usage of the shared spectrum. It features an intermediate spectrum auctioneer responsible for allocating resources to commercial WSPs' base stations (BS)s by running secure spectrum auctions. In order to insure truthfulness in the proposed spectrum auction, an optimal bidding mechanism is proposed to enable BSs (bidders) to determine their true bidding values. We also present a resource allocation based on CA approach to determine the BS's optimal aggregated rate allocated to each UE from both the BS's permanent resources and winning auctioned spectrum resources. / Ph. D.