A Large Cardinal is a type of infinite cardinal number that is larger than all smaller cardinals. These cardinals are significant in set theory, a branch of mathematical logic that studies sets, which are collections of objects. Large cardinals often have properties that cannot be proven within standard set theory, making them a topic of interest in advanced mathematics. Examples of large cardinals include inaccessible cardinals and measurable cardinals. The existence of large cardinals can lead to the development of new mathematical theories and insights. They play a crucial role in understanding the foundations of mathematics and the nature of infinity, influencing areas such as Zermelo-Fraenkel set theory and Gödel's incompleteness theorems.