Much of the data that is fueling current rapid advances in machine learning is high dimensional, structurally complex, and strongly nonlinear. This poses challenges for researcher intuition when they ask (i) how and why current algorithms work and (ii) what tools will lead to the next big break-though. Mathematicians working in topology, algebra, and geometry have more than a hundred years worth of finely-developed machinery whose purpose is to give structure to, help build intuition about, and generally better understand spaces and structures beyond those that we can naturally understand. Following on the success of the first TAG-ML workshop in 2022, this workshop will showcase work which brings methods from topology, algebra, and geometry and uses them to help answer challenging questions in machine learning. Topics include mathematical machine learning, explainability, training schemes, novel algorithms, performance metrics, and performance guarantees. All accepted papers will be included in an associated PMLR volume.