Book description: This book contains the shortest and simplest presentation of a novel pedagogical approach to relativistic quantum mechanics, and some transcendental implications of this approach for the fundamentals of physics and cosmology. This approach to relativistic quantum mechanics is based on the use of the Grave de Peralta (GP) equations. In this book, the solutions of the GP equations for the infinity one-dimensional well are used for discussing several transcendental topics of high interest about the fundaments of physics and cosmology. This includes the following topics: why the world surrounding us seems to be classical, why there is no more chemical elements in the Periodic Table, why there is not biological antimatter in our world, and why the cosmological constant is so small when compared with current relativistic quantum mechanics predictions.