A description of the geometry of space-time, in particular the theory of special relativity, with all the questions and issues explained without relying solely on formulas. The author shows that the geometry of space-time is indeed geometry, using actual constructions with which we are familiar from Euclidean geometry, and which admit exact demonstrations and proofs. He also uses the relation to projective geometry to illustrate the starting points of general relativity.This is not intended as a textbook aimed at introducing readers to the theory of relativity so they may calculate formally, but rather its aim is to show the connection with synthetic geometry - a first in books on special relativity.The book is written at an introductory (undergraduate) level, with the formal mathematics behind the constructions provided in the appendices. The novel presentation allows teaching staff to learn from it, too.