Matroid theory is a branch of mathematics that studies the concept of independence in sets. It generalizes the idea of linear independence from vector spaces to more abstract structures. A matroid consists of a finite set and a collection of subsets, called independent sets, that satisfy certain properties, allowing for the analysis of combinatorial structures. Matroids have applications in various fields, including graph theory and optimization. They help in understanding the properties of networks and can be used to solve problems like finding the minimum spanning tree in a graph. Key concepts in matroid theory include bases, circuits, and rank, which provide insights into the structure of independent sets.