This book offers a comprehensive exploration of Lorentz spaces, delving into key areas of mathematics, such as linear algebra, analytical geometry, differential geometry (including the theory of curves, the theory of surfaces), kinematic geometry, and manifolds, all from a Lorentzian perspective. It illustrates how these fundamental fields can be applied to Lorentzian geometry. This work is aimed at postgraduate students and researchers seeking to gain a thorough understanding of the fundamental concepts of Lorentzian geometry, with an emphasis on developing a strong background. To this end, the book serves as a guide for researchers interested in specializing in Lorentzian geometry and its related fields. Furthermore, to prevent confusion caused by inconsistent notations in the literature, it employs a rigorous and consistent notation throughout all chapters. With its clear and accessible language, the book provides researchers who wish to study Lorentzian geometry with a comprehensive understanding of the subject matter, while maintaining the integrity of notation. The book comprises nine chapters, each of which is accompanied by examples and detailed explanations to facilitate the comprehension of the topics covered. It is expected that this book, which also identifies and addresses some errors in the literature, will be a valuable reference for future studies seeking accuracy and precision.