This chapter explores the synergy of geometric, topological, and algebraic methods within the context of Neuro-Symbolic AI, a paradigm that aims to combine the learning capabilities of neural networks with the reasoning and interpretability of symbolic systems. As AI systems face increasingly complex data, traditional Euclidean-based methods often fall short in effectively capturing the intricate structures and relationships inherent in such data. Geometric methods, utilizing graphs and manifolds, extend the analytical capabilities of AI into non-Euclidean spaces, enabling sophisticated modeling of spatial relationships and networked data. Topological methods, particularly persistent homology, offer powerful tools for multi-scale feature analysis, revealing deep insights into the data’s intrinsic structure through the study of connected components, loops, and voids. Algebraic methods provide a robust framework for encoding symmetries and invariances, enhancing model robustness and generalization through group theory, rings, and fields. By integrating these advanced mathematical approaches, we develop unified frameworks that significantly enhance data representation and reasoning capabilities. This chapter details the complementary strengths of these methods, addresses current computational and scalability challenges, and highlights future research opportunities and practical applications in fields such as bioinformatics, robotics, and physics simulations. Through this integration, Neuro-Symbolic AI stands to achieve unprecedented levels of interpretability, efficiency, and intelligence, driving the next generation of AI advancements.