Perturbation theory is a mathematical method used to approximate solutions to a problem that is difficult to solve exactly. It is commonly used in physics, engineering, and other scientific disciplines to analyze complex systems where exact solutions are not readily available. In perturbation theory, the problem is broken down into a simple, solvable base case, known as the unperturbed problem, and a small additional term, known as the perturbation. The solution to the perturbed problem is then approximated as a series expansion based on the known solution to the unperturbed problem. This allows researchers to make accurate predictions about the behavior of the system, even when exact solutions are not possible. Perturbation theory is a powerful tool for studying a wide range of systems, from the behavior of atoms and molecules in quantum mechanics to the stability of celestial orbits in astrophysics. It is a versatile and widely used technique in scientific research, providing valuable insights and predictions that would otherwise be difficult to obtain.