 The Boltzmann, Gibbs, von Neumann, Schanen, BG, Entropy, as well as its continuous and quantum counterparts form the basis for the construction of the BG statistical mechanics. Recently, however, there has been a proliferation of natural, artificial, and social complex systems which do not conform to these principles. To address this issue, a new framework known as the non-extensive statistical mechanics was developed in 1988 based on the non-additive entropy. This entropy, denoted by SQ, is the cornerstone of a large number of mathematical, experimental, observational, and computational validations in the field of complexity. It also plays a key role in the study of plectics, as Murray Gilman called it. This article was authored by Konstantino Tsalis.