Geometric Measure Theory is a branch of mathematics that combines geometry and measure theory to study geometric objects and their properties. It focuses on the generalization of concepts like length, area, and volume to more complex shapes, particularly in higher dimensions. This field is essential for understanding the structure of sets and functions in mathematical analysis. One of the key concepts in Geometric Measure Theory is the Hausdorff measure, which extends the notion of measure to non-integer dimensions. This theory has applications in various areas, including calculus of variations, minimal surfaces, and geometric analysis, providing tools for solving problems in these fields.