A hypergraph generalizes a graph by allowing edges (hyperedges) to connect any number of nodes simultaneously, modeling group interactions that cannot be decomposed into pairwise relationships. Hypergraph Neural Networks (HGNN) extend message-passing GNNs via the incidence matrix H: node features aggregate across each hyperedge, then hyperedge features broadcast back — capturing higher-order structure. The normalized Laplacian Δ = D_v^{-1/2} H W D_e^{-1} H^T D_v^{-1/2} governs spectral convolution on hypergraphs. Applications span molecular interaction networks, co-authorship graphs, and visual scene understanding where objects participate in multi-way relations.