Personalized teaching is a key focus in modern education, aiming to meet individual student needs and improve learning efficiency. Traditional teaching methods struggle to address student differences in large-scale settings, leading to suboptimal personalized instruction. Recent advancements in generative artificial intelligence (GAI) and large language models (LLMs) offer significant support for the design and implementation of personalized teaching. This paper proposes a multilevel personalized teaching framework that integrates the core elements of the educational system, supporting personalized learning for students, optimizing teaching tasks for teachers, and enhancing resource management for higher education institutions. The framework operates from three perspectives: student, teacher, and institution, offering personalized services throughout the teaching process, including lesson planning, real-time adjustments, and post-class evaluations. The paper discusses the implementation approach based on technologies such as Mixture of Experts (MoE), Chain-of-Thought (CoT) reasoning, and dynamic prompting techniques, along with scenario examples and a validation scheme. The proposed framework provides theoretical support and practical guidance for universities to implement more effective personalized teaching based on AI technologies.