Introduction to the Geometrical Foundations of General Relativity: A Compendium of Tensor Calculus

This book is intended for physics students (undergraduate/transition to graduate) who want to prepare for lectures on general relativity. Some knowledge of linear algebra and analysis are required. This textbook starts with basic topics such as vector space and vectors (chapter 1), dual space and covectors (chapter 2), tensors (chapter 3), etc.. Great importance is always attached to the clarity of the explanations and derivations of the topics. 31 figures support these intentions. General relativity is in its deeper sense a geometric theory. Therefore, the emphasis in this textbook has been placed on understanding space in its geometric configuration. Space is a component of the representation of the physical real. And it is thus the stage on which the physical processes and procedures show themselves. Calculation tasks have been deliberately omitted. The focus is on understanding a topic. For this purpose, many examples and detailed extra introductions have been made. For exercises, there are enough examples in the relevant textbooks that can be used to deepen a topic. This book serves as a good basis for mastering tasks. If you have studied the book thoroughly, you will be prepared to start working on the physics of gravitation as described by general relativity.