The Mapper algorithm (Singh, Mémoli & Carlsson, 2007) creates a graph-based topological summary of high-dimensional data. Given a filter function f (e.g., x-coordinate, density), Mapper covers the range with overlapping intervals, clusters each preimage f⁻¹(Iᵢ) independently, and connects clusters that share points. The resulting graph reveals global topology (loops, branches, flares) invisible to linear methods like PCA. Landmark applications include discovering a new breast cancer subtype (Nicolau et al., 2011) and revealing a flare in NBA player statistics. Mapper captures the nerve of the covering, approximating the shape's topology via the nerve lemma.