The paper by Juan Maldacena proposes a method to calculate the expectation values of Wilson loop operators in large $N$ field theories, specifically focusing on $\mathcal{N} = 4$ 3+1 dimensional super-Yang-Mills. The method involves calculating the area of a fundamental string worldsheet in certain supergravity backgrounds. This approach is also extended to the case of coincident M-theory fivebranes, where the area of M-theory two-branes is considered. The paper discusses the computation for 2+1 dimensional super-Yang-Mills with sixteen supercharges, which is non-conformal. The energy of quark-antiquark pairs is calculated in these cases. The introduction reviews the relationship between the 't Hooft limit of large $N$ gauge theories and string theory, particularly for $\mathcal{N}=4$ super-Yang-Mills. The 't Hooft limit is defined as the limit where $N \to \infty$ while keeping $g_{YM}^2 N$ fixed, leading to a weakly coupled string theory on $AdS_5 \times S^5$. The paper then delves into the Wilson loop operator, which is related to the phase factor associated with the propagation of a very massive quark in the fundamental representation of the gauge group. The expectation value of the Wilson loop is shown to be proportional to the area of a fundamental string worldsheet in the supergravity background. The paper also discusses the relation to supergravity, where the expectation value of the Wilson loop is proposed to be proportional to the proper area of a fundamental string worldsheet. This is regularized by subtracting the mass of the W-boson, leading to a finite result. The calculation of the quark-antiquark potential is detailed, showing that the energy scales as $1/L$, indicating screening of charges. The paper also considers the case of non-constant angles for the quarks and the behavior of Wilson loops in non-conformal theories, such as 2+1 dimensional super-Yang-Mills with sixteen supercharges. Finally, the paper explores the application of this method to M-theory membranes, where Wilson "surface" observables are defined and calculated. The results are consistent with the expectations from conformal invariance.The paper by Juan Maldacena proposes a method to calculate the expectation values of Wilson loop operators in large $N$ field theories, specifically focusing on $\mathcal{N} = 4$ 3+1 dimensional super-Yang-Mills. The method involves calculating the area of a fundamental string worldsheet in certain supergravity backgrounds. This approach is also extended to the case of coincident M-theory fivebranes, where the area of M-theory two-branes is considered. The paper discusses the computation for 2+1 dimensional super-Yang-Mills with sixteen supercharges, which is non-conformal. The energy of quark-antiquark pairs is calculated in these cases. The introduction reviews the relationship between the 't Hooft limit of large $N$ gauge theories and string theory, particularly for $\mathcal{N}=4$ super-Yang-Mills. The 't Hooft limit is defined as the limit where $N \to \infty$ while keeping $g_{YM}^2 N$ fixed, leading to a weakly coupled string theory on $AdS_5 \times S^5$. The paper then delves into the Wilson loop operator, which is related to the phase factor associated with the propagation of a very massive quark in the fundamental representation of the gauge group. The expectation value of the Wilson loop is shown to be proportional to the area of a fundamental string worldsheet in the supergravity background. The paper also discusses the relation to supergravity, where the expectation value of the Wilson loop is proposed to be proportional to the proper area of a fundamental string worldsheet. This is regularized by subtracting the mass of the W-boson, leading to a finite result. The calculation of the quark-antiquark potential is detailed, showing that the energy scales as $1/L$, indicating screening of charges. The paper also considers the case of non-constant angles for the quarks and the behavior of Wilson loops in non-conformal theories, such as 2+1 dimensional super-Yang-Mills with sixteen supercharges. Finally, the paper explores the application of this method to M-theory membranes, where Wilson "surface" observables are defined and calculated. The results are consistent with the expectations from conformal invariance.