Nevanlinna theory is a branch of complex analysis that studies the value distribution of meromorphic functions, which are functions that can be expressed as the ratio of two holomorphic functions. Developed by Rolf Nevanlinna in the early 20th century, this theory provides tools to understand how often a function takes on certain values and how these values are distributed in the complex plane. The theory is particularly useful in fields like number theory and mathematical physics, as it connects the growth of functions to their zeros and poles. By analyzing these properties, mathematicians can gain insights into the behavior of complex functions and their applications in various scientific areas.