Einstein's theory of unusual relativity consists of electricity and magnetism in an easy, reasonable expansion of the relativity of Galileo and Newton. Its conclusions include time dilation, length contraction, and E=mc2 have changed intensely our thoughts of time and space, matter and energy.
Of course it is possible, you already travel in time towards the future at the rate on 1 second per second. Traveling towards the future at a different rate is not only possible, but also proven by experiments. The big question is time travel to the past. There is no way to do that in Special Relativity, as it would require superluminal motion. It is however allowed in General Relativity. It is unclear whether it will still be possible when quantum effects are taken into account, and there is current ongoing research on that.