Non-Abelian Gauge Theory is a framework in theoretical physics that describes the fundamental interactions between particles using gauge fields. Unlike Abelian theories, where the order of operations does not matter, non-Abelian theories involve symmetries that depend on the order of transformations. This leads to more complex interactions, which are essential for understanding the behavior of particles in the Standard Model of particle physics. A key example of a non-Abelian gauge theory is Quantum Chromodynamics (QCD), which describes the strong force that binds quarks and gluons together inside protons and neutrons. The gauge group associated with QCD is SU(3), reflecting the three types of color charge in quarks. Non-Abelian gauge theories are crucial for explaining phenomena such as particle collisions and the unification of forces at high energies.