Cantor's Set Theory, developed by Georg Cantor in the late 19th century, explores the concept of infinity and the different sizes of infinite sets. It introduces the idea of a set, which is a collection of distinct objects, and shows that some infinite sets, like the set of all integers, are smaller than others, such as the set of real numbers. One of Cantor's key contributions is the Cantor's diagonal argument, which demonstrates that there are more real numbers between 0 and 1 than there are natural numbers. This groundbreaking work laid the foundation for modern mathematics and has profound implications in various fields, including mathematical logic and theoretical computer science.