A Guide to Elementary Number Theory is a short exposition of the topics considered in a first course in number theory. It is intended for those who have had some exposure to the material before but have half-forgotten it, and also for those who may have never taken a course in number theory but who want to understand it without having to engage with the more traditional texts which are often extensive, and dense. Number theory has an impressive history, which this guide investigates. Rather than being a textbook with exercises and solutions, this guide is an exploration of this interesting and exciting field. Its important results are all included, usually with accompanying proofs: the Quadratic Reciprocity Theorem is proved as Gauss did it. The material has been chosen to be maximally broad whilst remaining concise and accessible.