Now that you have been introduced to the concepts of the theory, let's take a quick look at the relation between time travel and Special Relativity. If you remember the result from the twin paradox, you should agree that traveling into the future is possible, even at the speeds that our astronauts travel. Granted they would probably only be gaining a few nanoseconds, but when they return, the time on earth is ahead of their system time. Thus, they have returned to the future. As far as travelling back in time, Special Relativity is not as gracious as it is with moving forward. Let's take a look at this approach…
Many creative minds have wondered that since time slows down as you approach the speed of light, if you could find a way to travel faster than the speed of light, could you travel back in time? If I am to believe that special relativity is correct, then I am also to believe that the following events would occur. In order to travel faster than the speed of light, I assume that you would at some point have to travel at exactly the speed of light. For example, you can not travel 51 miles/hour without having traveled 50 miles/hour at some point, of course, this is providing that you were traveling 50 miles/hour or less to begin with. Now SR tells us that at the speed of light, time stops, your length contracts to nothing, and your resistance to acceleration becomes infinite requiring infinite energy (as observed by a frame of reference that is not in motion with the system). These conditions do not sound very conducive to life. Thus, I conclude that time travel into the past, using the concepts of SR, has some severe issues to overcome.