Just think if there is a law that states that the sum of all forces on an object is zero then there will be no motion in this world or universe. SO there is no such law.
Newton’s second law of motion states that if there are forces acting on a body then the net force (that would be vector sum of all forces) is equal to the product of the mass of the body and the acceleration induced by this net force. Often written as
$$\boldsymbol F_\mathrm{net} = m \boldsymbol a$$
Important to note that the acceleration is a result of force and not vice versa. While tackling problems that utilize Newton’s 2nd law of motion, one should first establish the left side of the equation by taking the vector sum of all forces and then equate with the RHS
The second law is often also stated as -
“The rate of change of momentum of an object is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force”. In the equation $F = ma$, if you write $a$ as $dv/dt$ and take $m$ inside to express it as $F = d(mv)/dt$, what you get is $F =$ rate of change of momentum where $mv$ is momentum of mass $m$.
However, Newton's law does not apply under 2 conditions -
One, if the object is moving at speeds that are close to or comparable with that of light. Under such conditions Einstein’s special theory of relativity explains the motion. Two, the size of the object is atomic - This then falls in the realm of quantum mechanics
You may like to see this video, made by me to understand the law better
NEWTON'S SECOND LAW OF MOTION