The normal distribution and its abstract counterparts are a cornerstone in the theory and practice of probability and statistics. Amongst many remarkable properties that they have are their numerous characterization properties and their manifold connections to other, sometimes unexpected, parts of probability. In this book, the author's aim is to present a readable and wide-ranging account of this subject. The reader will be introduced to important topics such as characteristic functions, conditional expectations, symmetries, and tail integration. What makes this book unique is its numerous sidetracks to explore other related topics including large deviations, strong mixing coefficients, the Wiener process, and probability on abstract spaces. Whilst the author assumes that the reader has a firm grounding in the basics of probability theory, it is intended to be read by graduate students and so there are many problems to help the reader gain a deeper understanding of this fascinating topic.