Over the last decade, topological and geometric data analysis (TGDA), a field concerned with using tools and methods from algebraic topology and geometry to analyze data, has seen rapid growth both in popularity among researchers/practitioners and in utility across many scientific domains such as biology, chemistry, dynamical systems, material sciences, and neuroscience. Researchers are driven by the paradigm that the shape of data leads to a much deeper understanding than that gained by other traditional methods when analyzing complex data. Modern advances in TGDA engage with statistics and machine learning tools, leading to new avenues for data science. For example, the great success of graph neural networks models tackling a wide range of problems, has led to a growing research activity in learning data on topological spaces modeled as manifolds, simplicial complexes, cell complexes and hypergraphs. The goal of this minisymposium is to disseminate developments at the interface of TDGA, statistics, and machine learning, and to project future next steps for this research field while fostering research interactions and discussions across the growing TDGA community. The programme of this minisymposium consists of part I and part II.