K-theory is a branch of mathematics that studies vector bundles and their properties. It provides a way to classify these bundles using algebraic techniques, allowing mathematicians to understand their structure and relationships. K-theory has applications in various fields, including topology, algebraic geometry, and even theoretical physics. One of the key concepts in K-theory is the K-group, which consists of equivalence classes of vector bundles over a topological space. By analyzing these groups, mathematicians can gain insights into the underlying geometry and topology of the space, leading to deeper understanding and new results in related areas.