This paper presents a comprehensive study of Meta Prompting, an innovative technique reshaping the utilization of large language models (LLMs), multi-modal foundation models, and AI systems in problem-solving and data interaction. Grounded in type theory and category theory, Meta Prompting emphasizes the structure and syntax of information over traditional content-centric methods. The paper explores the formal definitions of Meta Prompting (MP), sets it apart from Few-Shot Prompting, and underlines its effectiveness in various AI applications. A key focus is applying Meta Prompting for complex reasoning (MP-CR) tasks, showing how it effectively deconstructs intricate problems into simpler sub-problems, enhancing token efficiency, and enabling more equitable problem-solving comparisons, especially against few-shot prompting methods. Additionally, the paper introduces Meta Prompting for prompting tasks, allowing LLMs to self-generate new prompts in a recursive, metaprogramming-like manner. This approach marks a significant leap in AI's autonomous and adaptive capabilities. The paper also introduces the integration of Meta Prompting into multi-modal foundation model settings, tackling the challenges and opportunities of incorporating varied data types such as images, audio, and video within the structured Meta Prompting framework. Empirical experiments, including solving the Game of 24 tasks with 100\% success rate, demonstrate the MP-CR Agent's enhanced reasoning capabilities, achieving high accuracy and efficiency, and showcasing Meta Prompting's transformative impact on AI problem-solving.