Quasinormal modes (QNMs) of black holes are oscillations that occur when a black hole is perturbed. These modes are crucial for understanding the behavior of black holes in various contexts, including astrophysics and string theory. QNMs are characterized by complex frequencies, where the real part corresponds to the oscillation frequency and the imaginary part represents the damping rate. The study of QNMs helps in understanding the stability, thermodynamic properties, and hydrodynamic behavior of black holes. QNMs are determined by solving the wave equation for perturbations of black holes, which can be done using various methods such as the Mashhoon method, Chandrasekhar-Detweiler and shooting methods, WKB method, and others. These methods involve analyzing the behavior of perturbations near the black hole horizon and at infinity, with specific boundary conditions that ensure the physical consistency of the solutions. The analysis of QNMs has significant implications in different areas of physics. In astrophysics, QNMs are important for detecting gravitational waves from black holes, as the fundamental mode of QNMs dominates the signal. In string theory, QNMs are related to the AdS/CFT correspondence, which connects gravitational theories in anti-de Sitter space to conformal field theories in flat space. This connection allows for the study of strongly coupled systems, such as quark-gluon plasmas, through the properties of QNMs. QNMs also play a role in understanding the stability of black holes. The damping of QNMs indicates the stability of a black hole, while the presence of unstable modes suggests potential instabilities. The study of QNMs in higher-dimensional black holes and brane-world models provides insights into the behavior of black holes in different dimensions and the nature of extra dimensions in string theory. The methods for calculating QNMs involve solving the wave equations for different types of perturbations, such as scalar, vector, and tensor fields, in various black hole backgrounds. These methods include numerical and analytical techniques, with the WKB method being particularly useful for low-lying QNMs. The results from these methods are essential for understanding the dynamics of black holes and their interactions with their surroundings.Quasinormal modes (QNMs) of black holes are oscillations that occur when a black hole is perturbed. These modes are crucial for understanding the behavior of black holes in various contexts, including astrophysics and string theory. QNMs are characterized by complex frequencies, where the real part corresponds to the oscillation frequency and the imaginary part represents the damping rate. The study of QNMs helps in understanding the stability, thermodynamic properties, and hydrodynamic behavior of black holes. QNMs are determined by solving the wave equation for perturbations of black holes, which can be done using various methods such as the Mashhoon method, Chandrasekhar-Detweiler and shooting methods, WKB method, and others. These methods involve analyzing the behavior of perturbations near the black hole horizon and at infinity, with specific boundary conditions that ensure the physical consistency of the solutions. The analysis of QNMs has significant implications in different areas of physics. In astrophysics, QNMs are important for detecting gravitational waves from black holes, as the fundamental mode of QNMs dominates the signal. In string theory, QNMs are related to the AdS/CFT correspondence, which connects gravitational theories in anti-de Sitter space to conformal field theories in flat space. This connection allows for the study of strongly coupled systems, such as quark-gluon plasmas, through the properties of QNMs. QNMs also play a role in understanding the stability of black holes. The damping of QNMs indicates the stability of a black hole, while the presence of unstable modes suggests potential instabilities. The study of QNMs in higher-dimensional black holes and brane-world models provides insights into the behavior of black holes in different dimensions and the nature of extra dimensions in string theory. The methods for calculating QNMs involve solving the wave equations for different types of perturbations, such as scalar, vector, and tensor fields, in various black hole backgrounds. These methods include numerical and analytical techniques, with the WKB method being particularly useful for low-lying QNMs. The results from these methods are essential for understanding the dynamics of black holes and their interactions with their surroundings.