According to Einstein’s Special Theory of Relativity, the speed of light always remains constant at 186,000 miles per second regardless of whether it is gauged from a stationary reference point, a moving reference point or any other reference points, no object could travel faster than 186,000 miles per second (the speed of light itself) because the mass of the object would then be so great (infinitely great) that it could not accelerate anymore, on approaching the speed of light a moving object contracts in length in the direction of motion while a clock gauging the time slows down, at the speed of light the length of the moving object contracts to zero while the clock (and time) becomes at a standstill, and, importantly, the mass of an object multiplied by the square of the speed of light gives energy (E = MC2), i.e., mass could be converted to energy and vice versa; on approaching the speed of light the brain and bodily functions of a person slow down; observers do not agree on the simultaneity of events - two simultaneous events for one observer might not be simultaneous for another; in the Special Theory time-travel (in the space-time continuum) is an apparent possibility. A deeper look at the Special Theory of Relativity is presented in this paper, employing some strong, subtle and important mathematical reasoning in the process.