One purpose of this course is to provide an introduction to some aspects of hyperbolic geometry. Hyperbolic geometry is one of the richest areas of mathematics, with connections not only to geometry but to dynamical systems, chaos theory, number theory, relativity, and many other areas of mathematics and physics. Unfortunately, it would be impossible to discuss all of these aspects of hyperbolic geometry within the confines of a single lecture course. Instead, we will develop hyperbolic geometry in a way that emphasises the similarities and (more interestingly!) the many differences with Euclidean geometry (that is, the‘real-world’ geometry that we are all familiar with).
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