2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53281We review the structure of W_\infty algebras, their super and topological extensions, and their contractions down to (super) w_\infty. Emphasis is put on the field theoretic realisations of these algebras. We also review the structure of w_\infty and W_\infty gravities and comment on various applications of W_\infty symmetry.(24 pages)High Energy Physics - Theorytext