The book "Hyperbolic Geometry" deals with a range of topics related to hyperbolic geometry. The book covers Universal Hyperbolic Geometry, which provides a comprehensive understanding of the principles and properties of hyperbolic geometry. It explores Sydpoints and Finite Fields, highlighting their significance in the context of hyperbolic geometry. Additionally, the book introduces the elements of non-Euclidean geometry, demonstrating how it contributes to the development of the concept of rectilinear placement of points, particularly relevant for schoolchildren. Another intriguing aspect discussed in the book is the application of non-Euclidean geometry and defected structure for bodies with variable material composition. This exploration sheds light on the practical implications and real-world applications of hyperbolic geometry. Furthermore, the book explores the concept of Quantum Dark Energy, drawing insights from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos