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. This workshop will show-case work which brings methods from topology, algebra, and geometry and uses them to help answer challenging questions in machine learning. With this workshop we will create a vehicle for disseminating machine learning techniques that utilize rich mathematics and address core challenges described in the ICML call for papers. Additionally, this workshop creates opportunity for presentation of approaches which may address critical, domain-specific ML challenges but do not necessarily demonstrate improved performance on mainstream, data-rich benchmarks. To this end our proposed workshop will open up IMCL to new researchers who in the past were not able to discuss their novel but data set-dependent analysis methods.We interpret topology, algebra, and geometry broadly and welcome submissions ranging from manifold methods to optimal transport to topological data analysis to mathematically informed deep learning. Through intellectual cross-pollination between data-driven and mathematically-inspired communities we believe this workshop will support the continued development of both groups and enable new solutions to problems in machine learning.