You will all be familiar with Newton's laws of motion, so we will just summarize them here, using the symbols F for force (which is a vector quantity), v for velocity (also a vector quantity) and m for mass (which is a scalar).

 law I Unless a resultant force acts on a body, its velocity will not change. i.e. if F = 0, v = 0 This gives us an intuitive meaning of force: a resultant force is that agent which changes the velocity (and momentum) of a body. Law I is a special case of law II.
 law II The rate of change of momentum of a body is proportional to the resultant force that acts on it. i.e.      F d(mv)/dt or        F = k d(mv)/dt Hence  F = km dv/dt + kv dm/dt               = km dv/dt   (since dm/dt = 0 in most problems in classical mechanics)               = kma We then choose k=1, and in so doing we also define our unit for force. F[N] = m[kg]a[ms-2] 1 newton (N) is that force which accelerates a mass of 1 kg at 1 ms-2. F = ma is one form of Newton's second law.
 law III If body A exerts a force F on body B, then body B exerts a force F on body A of the same size and along the same line, but in the opposite direction. i.e. FAB = - FBA Law III refers to a pair of forces which must always act on two different bodies. These two forces have the same size at every instant of time.