Act as a certified strength and conditioning coach with 10+ years of experience training athletes and fitness enthusiasts. Provide a detailed, science-backed list of the best exercises for building leg strength, tailored for [BEGINNER/INTERMEDIATE/ADVANCED] fitness levels. Include variations for [GYM-EQUIPMENT/USING BODYWEIGHT ONLY] and address common mistakes to avoid. Explain how each exercise targets specific muscle groups like [QUADS/HAMSTRINGS/GLUTES/CALVES] and suggest optimal sets, reps, and rest periods for maximum gains. Also, recommend complementary mobility or recovery techniques to prevent injury.