This article explores the transformative impact of TDA when integrated with AIand machine learning within advanced manufacturing. TDA, a branch of computational topology, provides a framework for analysing complex, high-dimensional data by capturing the shape and structure of data in a way that is robust to noise and variability. The significance of TDA lies in its ability to reveal underlying patterns and relationships in manufacturing data that are otherwise difficult to discern. The purpose of this article is to highlight the synergy between TDA and AI, focusing specifically on their application in predictive maintenance and process optimization. Predictive maintenance leverages TDA's capacity to identify early signs of equipment failure by analysing historical performance data, thus enabling proactive interventions that minimize downtime and reduce maintenance costs. In process optimization, TDA assists in understanding and improving manufacturing processes by providing insights into the complex interactions between variables and their impact on production efficiency. The integration of TDA with AI enhances machine learning models by incorporating topological features, which improves the models' ability to predict and adapt to changing conditions. This combination not only enhances the accuracy of predictive analytics but also enables more effective and adaptive process control strategies. Through case studies and practical examples, the article demonstrates how these advanced analytical techniques can lead to significant improvements in manufacturing efficiency and reliability.