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This brief introduces the fundamental theory and development of managing radio resources using a water-filling algorithm that can optimize system performance in wireless communication. Geometric Water-Filling (GWF) is a crucial underlying tool in emerging communication systems such as multiple input multiple output systems, cognitive radio systems, and green communication systems. Early chapters introduce emerging wireless technologies and provide a detailed analysis of water-filling. The brief investigates single user and multi-user issues of radio resource management, allocation of resources, and energy harvesting. Effective algorithms demonstrate the incredible potential capabilities of water-filling mechanisms. This brief is designed for researchers and professionals working with resource management and wireless communications. Advanced-level students in computer science and engineering will also find the information valuable.