The study of CAT(0) cube complexes (and group actions on them) has become an important topic in group theory and topology in the last 20-30 years. CAT(0) cube complexes enjoy non-positive curvature properties similar to those in classical settings - such as non-positive sectional curvature in manifolds - yet they also have a rich combinatorial structure, similar to that in trees (but higher dimensional). Their study has led to many breakthroughs in group theory and topology, such as the resolution of the Virtual Haken conjecture in 3-manifold theory. During the class we will discuss a number of techniques for studying CAT(0) cube complexes, including CAT(0) geometry and the duality with pocsets. We will see methods for constructing group actions on cube complexes, and examine the interplay between the geometry of cube complexes and the algebraic/algorithmic properties of the groups that act on them. There will also be some discussion of special cube complexes and their group theoretic consequences.