When it comes to the measurement and observation of physical, biological, medical, economic, or social variables, the normal distribution is the most famous and widely applied law standing behind random phenomena. Often, being introduced as the important distribution , it is applied without a sufficient awareness of its statistical background and its limitations. This book reviews properties of the normal distribution in between a probability theoretical and a data analytical point of view, and is directed towards readers with at least basic knowledge in probability and statistics. It can be used for self-study purposes, conveying statistical principles behind inference based on data analysis. Emphasis is laid on the practicability of the presented methods, being mainly confined to the analysis of a single data set. Numerous graphics and examples with real and simulated data are included to illustrate the discussed topics. Mathematical derivations of the results are omitted in general.