The Standard Model is inconsistent with that of general relativity, to the point that one or both theories break down under certain conditions (for example within known space time singularities like the Big Bang and the centers of black holes beyond the event horizon). The appearance of singularities in any physical theory is an indication that something is wrong and that there is a need for new physics. Singularities can be avoided in GR and any field theory through the introduction of an efficient regularization procedure as this book directs. Regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for the possibility that "new physics" (beyond the SM) may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use. Therefore the main objective of this book is to discover new physics (Quantum Gravity) at those scales (or extra dimensions) which the General relativity theory and Quantum mechanics is unable to model. This has been achieved and remains the work of an experimenter to verify. While this is a new approach to quantum gravity, it reproduces the results in loop quantum gravity and string theory as the book indicates. This book provides a complete overview of quantum gravity from the frontiers of theoretical physics research for graduate students and researchers.