I've been wondering if I'd ever get a chance to talk about this. 
The idea of SPEED greater than lightspeed is probably inapplicable. The universe only has two speed regions. Less than c, and c. Above c, the definition of speed does not exist. 
But going FTL is merely our desire to arrive at a destination without taking a whole lifetime to make the journey. There are other ways. Such as intantenous transfer. It wouldn't violate Relativity because speed is not involved. 
My favourite method is the one created by Greg Bear in "Moving Mars". Check it out. Not only can you move planets. You can communicate instantly and even destroy anything you want within 10 billion km. Planets, suns, places..... All with just one device. It's rather complicated, but it's smaller and much cheaper to maintain than a starfleet.