Modular functions are special types of functions in mathematics that are defined on the complex numbers. They exhibit periodic behavior, meaning they repeat their values in a regular pattern. These functions are often studied in the context of number theory and have applications in various areas, including cryptography and string theory. One of the most famous modular functions is the j-invariant, which plays a crucial role in the theory of elliptic curves. Modular functions can be transformed under specific operations, making them useful for solving problems related to modular forms and congruences in mathematics.