This paper presents a calculation of the shear viscosity η of the strongly coupled N=4 supersymmetric Yang-Mills (SYM) plasma using the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. The shear viscosity is found to be η = π/8 N² T³, where N is the number of colors and T is the temperature. This result is derived from the absorption cross section of low-energy gravitons by a near-extremal black three-brane, which is shown to coincide with the area of the horizon in the zero frequency limit. The result is conjectured to hold for finite 't Hooft coupling, with η = f(g_YM² N) N² T³, where f(x) is a monotonic function that decreases from O(x⁻² ln⁻¹(1/x)) at small x to π/8 when x → ∞. The paper discusses the importance of transport coefficients in hot gauge theories, particularly in the context of the quark-gluon plasma. At weak coupling, these coefficients can be calculated perturbatively, but at strong coupling, nonperturbative methods are needed. The AdS/CFT correspondence allows for analytical calculations in strongly coupled gauge theories by relating them to classical gravity on the background of black branes. The shear viscosity is related to the absorption cross section of gravitons by black branes, which is calculated using the wave equation on the black brane metric. The solution to the radial wave equation shows that the absorption cross section at zero frequency is equal to the area of the horizon, leading to the result η = π/8 N² T³. This result is consistent with the entropy density of the plasma and highlights the role of scale invariance in the N=4 SYM theory. The paper concludes that the shear viscosity approaches a constant value in the large 't Hooft coupling limit, and that the AdS/CFT correspondence provides a powerful tool for computing transport coefficients in strongly coupled gauge theories. The results suggest that the shear viscosity can be expressed as η = f(g_YM² N) N² T³, where f(x) is a monotonic function that decreases from O(x⁻² ln⁻¹(1/x)) at small x to π/8 when x → ∞. This result has important implications for understanding the behavior of strongly coupled plasmas in high-energy physics.This paper presents a calculation of the shear viscosity η of the strongly coupled N=4 supersymmetric Yang-Mills (SYM) plasma using the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. The shear viscosity is found to be η = π/8 N² T³, where N is the number of colors and T is the temperature. This result is derived from the absorption cross section of low-energy gravitons by a near-extremal black three-brane, which is shown to coincide with the area of the horizon in the zero frequency limit. The result is conjectured to hold for finite 't Hooft coupling, with η = f(g_YM² N) N² T³, where f(x) is a monotonic function that decreases from O(x⁻² ln⁻¹(1/x)) at small x to π/8 when x → ∞. The paper discusses the importance of transport coefficients in hot gauge theories, particularly in the context of the quark-gluon plasma. At weak coupling, these coefficients can be calculated perturbatively, but at strong coupling, nonperturbative methods are needed. The AdS/CFT correspondence allows for analytical calculations in strongly coupled gauge theories by relating them to classical gravity on the background of black branes. The shear viscosity is related to the absorption cross section of gravitons by black branes, which is calculated using the wave equation on the black brane metric. The solution to the radial wave equation shows that the absorption cross section at zero frequency is equal to the area of the horizon, leading to the result η = π/8 N² T³. This result is consistent with the entropy density of the plasma and highlights the role of scale invariance in the N=4 SYM theory. The paper concludes that the shear viscosity approaches a constant value in the large 't Hooft coupling limit, and that the AdS/CFT correspondence provides a powerful tool for computing transport coefficients in strongly coupled gauge theories. The results suggest that the shear viscosity can be expressed as η = f(g_YM² N) N² T³, where f(x) is a monotonic function that decreases from O(x⁻² ln⁻¹(1/x)) at small x to π/8 when x → ∞. This result has important implications for understanding the behavior of strongly coupled plasmas in high-energy physics.