Newton's laws of motion

The statements of the laws
Newton's laws of motion describe the acceleration of massive objects. The modern understanding of Newton's three laws of motion is:

First Law
If no net force acts on a particle, then it is possible to select a set of reference frames, called inertial reference frames, observed from which the particle moves without any change in velocity.
Second Law
Observed from an inertial reference frame, the net force on a particle is proportional to the time rate of change of its linear momentum. Momentum is the product of mass and velocity. This law is often stated as F = ma (the force on an object is equal to its mass multiplied by its acceleration).
Third Law
Whenever a particle A exerts a force on another particle B, B simultaneously exerts a force on A with the same magnitude in the opposite direction. The strong form of the law further postulates that these two forces act along the same line.
In the given interpretation mass, acceleration and most importantly force are assumed to be externally defined quantities. This is the most common, but not the only interpretation: one can consider the laws to be definitions of these quantities. Notice that the second law only holds when the observation is made from an inertial reference frame, and since an inertial reference frame is defined by the first law, asking a proof of the first law from the second law is a logical fallacy.