Newton's first law of motion
In terms of force
In an inertial frame, if the net external force on a system is zero, the net acceleration of the system (which can be measured, for instance, via the acceleration of its center of mass) is zero. Thus, the center of mass of the system undergoes uniform linear motion.
For a single particle, this states that if the net external force on the particle is zero, the net acceleration of that particle is zero. Thus, the particle undergoes uniform linear motion.
In terms of momentum
The linear momentum version of Newton's first law of motion is: if the net external impulse on a system is zero, the linear momentum of the system does not change. As a special case, for a closed system, which is a system that does not experience any forces from outside, the linear momentum does not change. This law is termed the conservation of linear momentum.
Along a particular coordinate axis
The following is a version of Newton's first law along a particular axis: if the component along an axis of the net external force on a system is zero, the acceleration of the system has zero component along that direction.