In the thesis, we investigate the static potential between quarks in the SU(3) Yang-Mills theory on the lattice. Understanding the potential is crucial in formation of bound quark and antiquark states -- hadrons. We generate field configurations on the lattice by using the Hybrid Monte Carlo algorithm for the Wilson and Lüscher-Weisz lattice actions across different inverse coupling constants $\beta$ and lattice volumes $(L,L_{t})$. From these configurations, we calculate Wilson loops, which we analyze to determine the static potential $V(r)$ in the continuum limit. Our results demonstrate a linear rise in static potential at large distances, which is consistent with the phenomenon of confinement. In the continuum limit, both actions reproduce the same string tension, but the ultraviolet part of the potential is under slight tension, which we attribute to systematic errors in extracting the potential from the data. These findings substantiate the non-perturbative dynamics of quantum chromodynamics and contribute to the understanding of hadron structure.
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