Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers is extensively studied in the book. In particular an exhaustive solution of the twin paradox is given followed by a detailed exposition of space-time geometry and trigonometry. Finally an appendix on general properties of commutative hypercomplex systems with four unities is presented.