Let us begin
our explanation of how Newton changed our understanding of the Universe
by enumerating his Three Laws
of Motion.
Newton's First Law of Motion:
I. Every object in a state of uniform motion tends to remain in that
state of motion unless an external force is applied to it.

This we recognize as essentially
Galileo's concept of inertia, and this is often
termed simply the "Law of Inertia".
Newton's Second Law of Motion:
II. The relationship between an object's mass m, its acceleration
a,
and the applied force F is
F = ma.
Acceleration and force are vectors (as indicated by their symbols being
displayed in slant bold font); in this law the direction of the force
vector is the same as the direction of the acceleration vector.

This is the most powerful of Newton's three Laws, because it allows quantitative
calculations of dynamics: how do velocities change when forces are applied.
Notice the fundamental difference between Newton's 2nd Law and the dynamics of
Aristotle: according to Newton, a force causes only a
change in
velocity (an acceleration); it does not maintain the velocity as Aristotle
held.
This is sometimes summarized by saying that under Newton,
F =
ma, but under Aristotle
F = mv, where
v is the velocity.
Thus, according to Aristotle there is only a velocity if there is a force, but
according to Newton an object with a certain velocity maintains that
velocity
unless a force acts on it to cause an acceleration (that is,
a change in the velocity). As we have noted earlier in conjunction with the
discussion of
Galileo,
Aristotle's view seems to be
more in accord with common sense, but that is because of a failure to
appreciate
the role played by frictional forces. Once account is taken of
all forces
acting in a given situation it is the dynamics of
Galileo and Newton, not of Aristotle, that are
found to be in accord with the observations.
Newton's Third Law of Motion:
III. For every action there is an equal and opposite reaction.

This law is exemplified by what happens if we step off a boat onto the bank of
a lake: as we move in the direction of the shore, the boat tends to move in
the opposite direction (leaving us facedown in the water, if we aren't
careful!).