Index Theory is a branch of mathematics that studies the relationship between the solutions of differential equations and the topology of the underlying space. It provides tools to understand how the properties of a space can influence the behavior of functions defined on it, particularly in the context of manifolds and operators. One of the key concepts in Index Theory is the index of an operator, which is a numerical value that represents the difference between the dimensions of the kernel and the cokernel of the operator. This theory has applications in various fields, including geometry, physics, and engineering, helping to solve complex problems related to differential equations.