Relativity and quantum mechanics are fundamentally di erent theories that have di erent formulations. It is not just a matter of scienti c terminology; it is a clash of genuinely incompatible descriptions of reality. Relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Relativity and Quantum Mechanics emphasizes on the relativity theory and scienti c principles that explains the behavior of matter and its interactions with energy on the scale of atoms and subatomic particles. First chapter provides an introduction to the theory of relativity of non-inertial systems and mechanics of the universe. In second chapter, we present a study of application of the PQL in resolution of phenomena of physical systems that involve concepts of the Relativity Theory. In third chapter, we present a study of application of the PQL in resolution of phenomena of physical systems that involve concepts of the Relativity Theory and the correlation of these e ects with the Newtonian Universe and Quantum Mechanics. Fourth chapter presents a theory provides an evidence that the time cannot be relative as stated by Theory of General Relativity. In fth chapter, we study the most important anomalies that are part of the foundations of general relativity with the goal of promoting the call period of transition that is previous to scienti c revolution. In sixth chapter, we outline a non-perturbative quantum relativity theory. Seventh chapter presents on the general relativity as the classical limit of the renormalizable gauge theory of volume preserving di eomorphisms. Eighth chapter highlights on the fundamental assumptions of the theory of relativity. The purpose of ninth chapter is to present for the rst time an elementary summary of a few recent results obtained through the application of the formal theory of partial di erential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Within the tenth chapter, we assume that the extent of the particle has a real physical meaning and can be described in terms of a certain internal charge distribution. The eleventh chapter aims at de ning a new concept of carcinogenesis and tumor progression. The aim of twelfth chapter is to give analysis of the quantum mechanics and relativity within the principles of classic energy conservation law and to describe main features of these theories within alternative concept of discrete energy conservation. Thirteenth chapter explores on the ‘computational uni ed field theory and fourteenth chapter reveals on correspondences of scale relativity theory with quantum mechanics. The physical nature of wave/particle duality is described in fteenth chapter. Theory of elementary particles based on Newtonian mechanics is presented in sixteenth chapter. The seventeenth chapter is composed of two parts. The rst part includes a general scheme of constructing the nonrelativistic quantum mechanics of a bound system with FE. In the second part of the chapter we consider the problem of a quantum harmonic oscillator with fundamental environment. Theoretical validation of the computational uni ed field theory is described in last chapter.
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