Modular forms are complex functions that are defined on the upper half of the complex plane and exhibit specific symmetry properties. They are important in number theory and have applications in various areas of mathematics, including algebraic geometry and cryptography. Modular forms can be thought of as a generalization of periodic functions, and they are often studied in relation to elliptic curves. These functions can be classified into different types, such as cusp forms and newforms, based on their behavior at certain points. Modular forms are connected to automorphic forms and play a crucial role in the proof of Fermat's Last Theorem through the work of Andrew Wiles.