Do gravitational waves really travel in "nothing"? How does a Gravitational wave create ripple in the fabric of space, if space itself is an empty and it is made-up of nothing. Through out my academic life in school, I was told that space is made-up of nothing. 

If so, then in which medium waves travel? 

If they do indeed travel in "nothing", how is that possible?
Well, space isn't really nothing.

Empty space (properly spacetime), also called the vacuum, is pretty complicated in modern physics. All of the fields, like the electromagnetic field and the electron/Dirac field, are there whether or not there are any particles (photons or electrons). The particles are vibrations of the fields – or to put it another way, they're vibrations of the vacuum.

Although people tend to say that gravity is different from everything else, it isn't really very different. The vacuum has a "shape", and it can vibrate in various ways. Some of the vibrational modes are gravitational waves. Others correspond to electrons, photons, etc. The details are complicated but the idea is simple.

The vacuum is different from an ordinary wave medium in some ways. Most importantly, it doesn't have a state of motion: you can't detect a "vacuum wind" or "vacuum current" resulting from moving through the vacuum. But if you keep that imporant caveat in mind, then the analogies of a "fabric of spacetime" or of gravitational waves as waves on the surface of the ocean are not so inaccurate.