Extremal Graph Theory is a branch of mathematics that studies the maximum or minimum number of edges in a graph that satisfies certain properties. It focuses on understanding how the structure of a graph influences its edge count, often exploring questions related to graph density and subgraph presence. One of the key results in this field is Mantel's Theorem, which determines the maximum number of edges in a triangle-free graph. Researchers in extremal graph theory often use combinatorial techniques and inequalities to derive results, contributing to broader areas such as combinatorics and theoretical computer science.