Newton established his three laws of motion to do what?

Newton established his three laws of motion to understand the motion of objects in a systematic way [ same thing as all Scientists did for human's curiosity ].

His three laws of motion are as follows:

First Law: -  An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Second Law: -  The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Third Law: - For every action, there is an equal and opposite reaction

Hope this helps!