The maths (and physics) of gravitational waves

Abstract: 

The direct detection of gravitational waves has been touted as one of the greatest scientific discoveries.But what are gravitational waves, and how were they detected?

Here, I will review the concepts and ideas behind Einstein's general theory of relativity, including the notion of space-time, the stuff that does the waving in a gravitational wave.We will also consider the interaction of a gravitational wave with matter, and look at how we deduce that the wave was formed by the collision by two massive black holes.