Algebraic K-Theory is a branch of mathematics that studies algebraic structures using tools from topology and abstract algebra. It focuses on understanding the relationships between different algebraic objects, such as rings and modules, by associating them with topological spaces. This approach helps mathematicians analyze properties that are invariant under certain transformations. One of the key concepts in Algebraic K-Theory is the K-groups, denoted as K₀, K₁, and K₂, which capture information about vector bundles and projective modules. These groups have applications in various areas, including number theory, geometry, and homological algebra, providing insights into the structure of algebraic objects.