Machine Learning Tutorial Lecture The use of algebraic methods—specifically group theory, representation theory, and even some concepts from algebraic geometry—is an emerging new direction in machine learning. The purpose of this tutorial is to give an entertaining but informative introduction to the background to these developments and sketch some of the many possible applications, including multi-object tracking, learning rankings, and constructing translation and rotation invariant features for image recognition. The tutorial is intended to be palatable by a non-specialist audience with no prior background in abstract algebra.