**TopoX: A Suite of Python Packages for Machine Learning on Topological Domains** **Authors:** Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahim Aljabea, Ruben Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Meenal Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Meißner, Soham Mukherjee, Alexander Nikitin, Theodore Papamarkou, Jaro Prilepok, Karthikeyan Natesan Ramamurthy, Paul Rosen, Aldo Guzmán-Sáenz, Alessandro Salatiello, Shreyas N. Samaga, Simone Scardapane, Michael T. Schaub, Luca Scofano, Indro Spinelli, Lev Telyatnikov, Quang Truong, Robin Walters, Maosheng Yang, Olga Zaghen, Ghada Zamzmi, Ali Zia, Nina Miolane **Abstract:** TopoX is a Python software suite designed for machine learning and deep learning on topological domains, extending traditional graph-based methods to hypergraphs, simplicial, cellular, path, and combinatorial complexes. It consists of three main packages: TopoNetX, TopoEmbedX, and TopoModelX. TopoNetX facilitates the construction and computation on these domains, including handling nodes, edges, and higher-order cells. TopoEmbedX provides methods to embed topological domains into vector spaces, similar to graph-based embedding algorithms. TopoModelX, built on PyTorch, offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The suite is extensively documented and unit-tested, available under the MIT license. **Keywords:** topological deep learning, topological neural networks, graph neural networks, machine learning, Python packages. **Introduction:** Deep learning traditionally operates within Euclidean domains, but geometric deep learning (GDL) extends this to non-Euclidean data. Topological Deep Learning (TDL) explores models beyond traditional graph-based abstractions, processing data with multi-way relations. TopoX aims to address the lack of accessible software libraries for deep learning models with higher-order structures. It provides foundational code, user-friendly algorithms, and a unified API for topological domains, enhancing interoperability, productivity, and collaboration. **Implementation Overview:** - **TopoNetX:** Organized into *classes*, *algorithms*, and *transform* modules, it supports various topological domains and computations. - **TopoEmbedX:** Supports representation learning for all topological domains**TopoX: A Suite of Python Packages for Machine Learning on Topological Domains** **Authors:** Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahim Aljabea, Ruben Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Meenal Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Meißner, Soham Mukherjee, Alexander Nikitin, Theodore Papamarkou, Jaro Prilepok, Karthikeyan Natesan Ramamurthy, Paul Rosen, Aldo Guzmán-Sáenz, Alessandro Salatiello, Shreyas N. Samaga, Simone Scardapane, Michael T. Schaub, Luca Scofano, Indro Spinelli, Lev Telyatnikov, Quang Truong, Robin Walters, Maosheng Yang, Olga Zaghen, Ghada Zamzmi, Ali Zia, Nina Miolane **Abstract:** TopoX is a Python software suite designed for machine learning and deep learning on topological domains, extending traditional graph-based methods to hypergraphs, simplicial, cellular, path, and combinatorial complexes. It consists of three main packages: TopoNetX, TopoEmbedX, and TopoModelX. TopoNetX facilitates the construction and computation on these domains, including handling nodes, edges, and higher-order cells. TopoEmbedX provides methods to embed topological domains into vector spaces, similar to graph-based embedding algorithms. TopoModelX, built on PyTorch, offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The suite is extensively documented and unit-tested, available under the MIT license. **Keywords:** topological deep learning, topological neural networks, graph neural networks, machine learning, Python packages. **Introduction:** Deep learning traditionally operates within Euclidean domains, but geometric deep learning (GDL) extends this to non-Euclidean data. Topological Deep Learning (TDL) explores models beyond traditional graph-based abstractions, processing data with multi-way relations. TopoX aims to address the lack of accessible software libraries for deep learning models with higher-order structures. It provides foundational code, user-friendly algorithms, and a unified API for topological domains, enhancing interoperability, productivity, and collaboration. **Implementation Overview:** - **TopoNetX:** Organized into *classes*, *algorithms*, and *transform* modules, it supports various topological domains and computations. - **TopoEmbedX:** Supports representation learning for all topological domains