2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73188We describe some of the machinery behind recent progress in establishing infinitely many arithmetic progressions of length $k$ in various sets of integers, in particular in arbitrary dense subsets of the integers, and in the primes.38 pages, no figures, submitted, El Escorial conference proceedings. These lectures are oriented towards a harmonic analysis audienceNumber TheoryDynamical Systems11N13, 11B25, 374A5text