Is gravity made of particles or waves?
Gravity can't be described in terms of either particles or waves.
Isaac Newton described gravity as an attractive force between masses. This is a good approximation but it left many questions such as how the force is propagated.
Then came the theory of relativity. The universe was seen as three dimensional space and time as a a steady flow from past to future. We now know that the universe can be described in terms of four dimensional space time.
Albert Einstein's field equations describe gravity.
This apparently simple equation is actual ten second order partial differential equations which are very difficult to solve. The
Curved spacetime causes time to slow down. Gravity is a consequence of this. So, gravity is not a force. It is a consequence of spacetime being curved.
General relativity also predicted gravity waves. These have recently been detected. When two massive objects such as black holes collide they send ripples through spacetime. These waves are very small due to the fact that spacetime is hard to bend.