``Moving clocks run slow”, E = mc2 , warped spacetime, black holes: Most people have heard of these words, but what do they mean? Where did the ideas come from? Are they speculation or fact? How do we know? Of what use are they? How have they shaped our lives? In this module we will retrace the key ideas that led Einstein to his formulation of the Special Theory of Relativity, and how the concepts evolved through various personalities to produce the elegant spacetime version of the theory, culminating in the General Theory of Relativity. Along the way we will see the practical application of the scientific method and clarify common misconceptions of the theory. We will also study the impact Relativity has had on science, technology, philosophy and culture, and have a peek at the research frontier, where gravity and quantum theory meet, to be aware of open problems. Synopsis Einstein’s insight was that time must be relative, in contrast to Newton’s assumption of an absolute time. Time dilation (“moving clocks run slow”) is easily derived from Einstein’s postulates and it immediately implies a range of related effects such as the relativity of simultaneity and length contraction. These phenomena are seen to be interconnected through the formulation of a Minkowskian spacetime, which unites, and generalizes, Euclid’s space with Newton’s time. A further generalization leads to the General Theory of Relativity which shows gravity to be an effect of a dynamical curved spacetime, the framework for cosmology.