When a stone is thrown in the water say pond, tank etc. you have noticed that many small waves of water are formed which moves away from the point where stone hits the water. These are known as ripples.
Water in liquid state is not fixed sheet so it can easily change the shape. When a stone or an object is thrown into the water some energy transformation takes place moreover a particular volume of water gets displaced which is equal to the volume of the stone or the object that is thrown in water. Water in liquid state does not get compressed but depressed and is forced up. After reaching its original level it goes on somewhat further and starts moving to the other sides which lead to the formation of ripples.
The size of ripples depends on the energy of the moving object. When the water moves backward to fill the displaced water it is known as secondary ripples. When the outward moving ripple strikes with inward moving ripple then they eject a drop of water which when again hits the water surface forms another chain of water ripples which are small than the previous one.
These deformations on the surface of water can be explained by the mathematical equations which are very complex ones. These equations give the solution for small deformations and well behaved waves.