Moduli Theory is a branch of mathematics that studies families of geometric objects by classifying them according to certain parameters, known as moduli. These parameters help to understand how different objects can vary while still sharing common features. For example, in algebraic geometry, moduli spaces can classify curves or surfaces based on their shapes and properties. One of the key applications of Moduli Theory is in the study of Riemann surfaces and vector bundles. By analyzing these moduli spaces, mathematicians can gain insights into the structure and relationships of various mathematical objects, leading to deeper understanding in fields like number theory and string theory.