The increasing penetration of inverter-based renewable energy sources has fundamentally altered the dynamic behavior of modern power systems by displacing conventional synchronous generation. Reduced system inertia, higher rates of change of frequency, modified fault responses, and complex voltage regulation have emerged as critical stability challenges in low-inertia grids. This paper presents a comprehensive study of power system stability under high renewable energy penetration through a structured literature review, a unified methodological framework, and a realistic transmission-level case study. The proposed framework integrates grid characterization, component and control modeling, multi-domain stability assessment, contingency analysis, and coordinated mitigation strategies using both phasor-domain and electromagnetic transient simulations. A three-zone network with varying levels of renewable integration is analyzed to quantify impacts on frequency, voltage, and small-signal stability following severe contingencies. Results demonstrate that stability degradation increases nonlinearly with renewable share in baseline grid-following configurations. The deployment of grid-forming inverter controls, synthetic inertia, and fast frequency response from battery energy storage significantly improves system performance by reducing RoCoF, restoring frequency nadir, and enhancing voltage recovery. Eigenvalue analysis further confirms improved damping of critical interaction modes. The findings highlight the necessity of hybrid control architectures and coordinated mitigation strategies to ensure reliable operation of future power systems with high renewable penetration.