To begin to understand this question you must first understand what light itself is. A seemingly obvious notion at first, it is the very thing that allows us to observe our surroundings, but you must also understand how light works.
Thanks to the power of todays communication technologies, it is becoming increasingly common knowledge that light does not travel at infinite speeds. In fact, the finite speed of light is 186,000 miles per second. This was first discovered by Ole Christensen Roemer in 1676 who studied Jupiter’s moons orbital patterns. He discovered the closer we are to Jupiter in space, the earlier moons appeared from behind it. At times when we are far from Jupiter, the moons appear later from behind it. His conclusions had birthed the speed of light.
Although, his actual work led him to believe the speed of light was around 140,000 miles per second, however, modern technology has allowed us to determine a more accurate speed.
So, we would need to travel at this speed to travel faster than light itself. So the answer to our original question is, quite bluntly, no.
To give you examples of our own records, the fastest unmanned vehicle is the HTV-2, that travelled at 13,201 miles per hour. The fastest manned vehicle is the North American X-15, piloted by William J. Knight, travelling 4,510 miles per hour.
However, to reach a speed of 186,000 miles per second (or 669,600,000 miles per hour) the factors of an engines power or a humans piloting skills are shot out of the window (not literally, of course).
Light can travel at such speeds because it has no mass, as it is made up of photons which equally have no mass. In Stephen Hawking’s, A Brief History of Time, he wrote than this is explained in Albert Einstein’s famous theory E = mc² (E = energy, m = mass, c = speed of light).
Einstein’s law was that nothing may travel faster than the speed of light. It is difficult to simplify this process but the more energy an object uses (say a car engine) this will add to its mass, making it harder for it to keep increasing its speed (resulting in a car only being able to reach a top speed and not forever accelerating faster and faster). This means than light, and other waves of no mass, can travel at or faster than the speed of light.
This puts a rather dull dousing on the fantasy of galactic-light-speed-space-travel like in Star Wars, but also confirms we cannot travel faster than time itself as light allows us to experience time, however, that is a lesson for another day…