In a dynamic computing environment, such as the Grid, resource management plays a crucial role in making distributed resources available on demand to anyone from anywhere at any time without undermining resource autonomy. This becomes an art when dealing with heterogeneous resources distributed under multiple trust domains spanning across the Internet. Today, Grid execution environments provide abstract workflow descriptions that need a dynamic mapping to actual deployments, further accentuating the importance of resource management in the Grid. This monograph outlines the boundaries of Grid resource management, identifies research challenges, and proposes new solutions with innovative techniques for on-demand provisioning, automatic deployments, dynamic synthesis, negotiation-based advance reservation, and capacity planning of Grid resources. The Grid capacity planning is performed.