  Following the development of the special theory of relativity in 1905,
Minkowski proposed a unified space and time structure consisting of three space
dimensions and one time dimension, with relativistic effects then being natural
consequences of this spacetime geometry. In this paper, we illustrate how
Clifford's geometric algebra that utilizes multivectors to represent spacetime,
provides an elegant mathematical framework for the study of relativistic
phenomena. We show, with several examples, how the application of geometric
algebra leads to the correct relativistic description of the physical phenomena
being considered. This approach not only provides a compact mathematical
representation to tackle such phenomena, but also suggests some novel insights
into the nature of time.
