Study of topological spaces using algebraic tools. Aim is to find the algebraic invariants to spaces in a way that captures essential topological properties, particularly those preserved under continuous deformations (Homotopy Theory equivalence).
It converts geometric problems into algebraic ones by associating algebraic objects to spaces and homotopic maps. These constructions are designed to be invariant under homotopy, so that homotopy-equivalent spaces yield the same algebraic data. In doing so, it can simplify complex geometric questions into tractable algebraic computaitons.