Automorphic forms are complex mathematical objects that arise in the study of number theory and representation theory. They generalize the concept of modular forms, which are functions that exhibit specific symmetry properties under transformations of the complex upper half-plane. Automorphic forms can be defined on more general spaces, such as symmetric spaces or adelic groups, and they play a crucial role in understanding the relationships between different areas of mathematics. These forms are particularly important in the Langlands program, a set of conjectures connecting number theory and representation theory. Automorphic forms help in studying L-functions, which encode deep arithmetic information. They also have applications in various fields, including algebraic geometry and mathematical physics, making them a central topic in modern mathematics.