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Algebraic topology is a branch of mathematics that is uses tools of from abstract algebra to study of spaces (topological spaces and maps).

In algebraic topology, we investigate spaces by mapping them to algebraic objects such as groups, and thereby bring into play new methods and intuitions from algebra to answer topological questions.

**Branches of Algebraic Topology**

Homotopy groups, Homology, Cohomology, Manifolds, Knot theory and Complexes are the main branches of algebraic topology

**Applications of Algebraic Topology**

Algebraic topology is used in medical imaging, such as CT scans, to reconstruct three-dimensional shapes from cross-sectional (tomographic) data. Homotopy is used a lot in differential equations and machine learning algorithms, while homology is used in clustering, shape comparison, and partitioned regression.

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