The normal and Student’s t distributions are two of the most important distributions in statistics. These distributions have been extensively studied and used by many researchers since their discoveries. This book reviews the normal and Student’s \(t\) distributions, and their applications. These studies involve some preliminaries on random variables and distribution functions, which are defined below (in Sect. 1.1), (for details, see Lukacs 1972, Dudewicz and Mishra 1988, Rohatgi and Saleh 2001, Severini 2005, and Mukhopadhyay 2006, among others). Some special functions and mathematical results will also be needed, which, for the sake of completeness, are given below (in Sect. 1.2), (for details, see Abramowitz and Stegun 1970, Lebedev 1972, Prudnikov et al. 1986, and Gradshteyn and Ryzhik 2000, among others).