Algebraic Topology
Algebraic Topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The subject focuses on the study of algebraic invariants that classify topological spaces up to homeomorphism, with a primary focus on homotopy groups and cohomology rings. Algebraic Topology has deep connections with many areas within Mathematics including Differential Geometry, Number Theory, and Algebraic Geometry, as well as areas outside of Mathematics such as Physics and Computer Science. In the hierarchy "Science/Mathematics/Algebraic Geometry", Algebraic Topology can be seen as a tool to study and understand the topological properties of algebraic varieties that arise in Algebraic Geometry, by associating algebraic invariants to these spaces. This allows for a more detailed analysis of their structure and behavior.