2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141216In our recent paper arXiv:0704.1185 [hep-th], we presented the differential geometry of five-dimensional N=1 anti-de Sitter superspace AdS^{5|8}=SU(2,2|1)/SO(4,1) x U(1) and developed the harmonic and the projective superspace settings to formulate off-shell supersymmetric theories in AdS^{5|8}. Here we give a brief review of the geometry and the harmonic superspace construction, and also elaborate on vector supermultiplets.4 pages, LaTeX, Contribution to the proceedings of the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'07), Dubna, July 30-August 4 2007High Energy Physics - Theorytext