The increasing integration of power-electronics-interfaced distributed energy resources (DERs) is transforming microgrids, offering flexibility while introducing challenges in modeling, control, and stability. This chapter provides a comprehensive study of these issues, focusing on inverter-based microgrids. Microgrids are introduced with an emphasis on their key features, operational flexibility, and challenges arising from power-electronics-based generation. The mathematical modeling of inverters in the d-q frame is discussed, along with the widely adopted double-loop control strategy for regulating voltage and current dynamics. Microgrid modeling using differential–algebraic equations (DAEs) is explored, and droop control is presented as a fundamental decentralized method for power-sharing and voltage-frequency regulation. Finally, small-signal stability analysis is examined, identifying key factors affecting microgrid stabilityMicrogrid stability analysis and strategies for mitigating instabilities. By integrating power electronicsPower electronics in energy systems, control theory, and stability analysis, this chapter provides a practical framework for understanding and improving microgrid operation, offering valuable insights for researchers and engineers working on next-generation power systems.