Since the late 1800's, scientists, mathematicians, philosophers, and science-fiction writers have been fascinated with the concept that there exists an extra spatial dimension perpendicular to our usual three dimensions (up-down, left-right, and forward-backward) of geometric space. This is related to, but different than, treating time as a fourth dimension as in the space-time continuum of Albert Einstein's special theory of relativity. In this talk, we will discuss the geometric basics, history, and multi-disciplinary aspects of this 'notorious' Fourth Dimension!