We present a many-body calculation of the band structure and optical spectrum of the layered hybrid organicinorganic halide perovskites in the Ruddlesden-Popper phase with the general formula A 2 A nâ1 M n X 3n+1 , focusing specifically on the lead iodide family. We calculate the mean-field band structure with spin-orbit coupling, quasiparticle corrections within the GW approximation, and optical spectra using the Bethe-Salpeter equation. The model is parameterized by first-principles calculations and classical electrostatic screening, enabling an accurate but cost-effective study of large unit cells and corresponding thickness-dependent properties. A transition of the electronic and optical properties from quasi-two-dimensional behavior to three-dimensional behavior is shown for increasing n and the nonhydrogenic character of the excitonic Rydberg series is analyzed. The thickness-dependent 1s and 2s exciton energy levels are in good agreement with recently reported experiments and the 1s exciton binding energy is calculated to be 302 meV for n = 1, 97 meV for n = 5, and 37 meV for n = â (bulk MAPbI 3 ).Hybrid organic-inorganic perovskites (HOIPs) are promising photovoltaic materials, most recently showing a high power conversion efficiency of over 24%. 1 A three dimensional bulk HOIP AMX 3 can be transformed into a layered HOIP in the Ruddlesden-Popper phase A 2 A nâ1 M n X 3n+1 by substituting a small organic cation A + by a bulkier one A + .Common choices for the small organic cation are A + =CH 3 NH + 3 , NH + 4 ; for the bulkier cation are A + =C 4 H 9 NH + 3 , C 6 H 5 C 2 H 4 NH + 3 ; for the metal are M 2+ =Sn 2+ , Pb 2+ ; and for the halide are X â =Cl â , I â , Br â . A major drawback of the 3D HOIPs for photovoltaics is their relatively fast degradation when exposed to air, moisture, and light; in contrast, the layered HOIPs are more stable while maintaining high power conversion efficiencies under working conditions. 2,3 The optical properties of layered HOIPs can also be easily controlled by composition, 4 enhancing their flexibility for a variety of optoelectronic applications. Unlike the van der Waals materials -a prototypical family of layered materials including graphene, hexagonal boron nitride, and the transition-metal dichalcogenides -the layered HOIPs have sublayers that are covalently bonded. This distinct property makes the layered HOIPs an insightful mixeddimensional platform for investigating the transition of optoelectronic properties from two dimensional to three dimensional.The n-dependent properties of layered HOIPs have been experimentally investigated, especially during the last five years, 5-9 including mechanically exfoliated thin sheets of a layered HOIP. 10,11 Early theoretical investigations of the optical properties of layered HOIPs were performed using the effective mass approximation, giving good estimates for the exciton binding energy and a qualitative explanation of the essential physics. 5,12-14 For a quantitative analysis, ab initio approaches such as density functional...