Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book discusses the mathematical tools that are essential to describe the theory and its physical consequences. It aims at answering the following questions: Why did Newtonian theory become inappropriate to describe the gravitational field; and why do we need to introduce geometrical objects, like the metric tensor or the Christoffel symbols, to describe the gravitational field; and what is the role of the Equivalence Principle in this new geometrical framework. The book rigorously defines manifolds, vectors, tensors, and formulates Einstein’s equations after introducing the principle of general covariance.