We report 65 tesla magneto-absorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor WSe2. The strongly field-dependent and distinct energy shifts of the 2s, 3s, and 4s excited neutral excitons permits their unambiguous identification and allows for quantitative comparison with leading theoretical models. Both the sizes (via low-field diamagnetic shifts) and the energies of the ns exciton states agree remarkably well with detailed numerical simulations using the non-hydrogenic screened Keldysh potential for 2D semiconductors. Moreover, at the highest magnetic fields the nearly-linear diamagnetic shifts of the weakly-bound 3s and 4s excitons provide a direct experimental measure of the exciton's reduced mass, mr = 0.20 ± 0.01 m0.The burgeoning interest in atomically-thin transitionmetal dichalcogenide (TMD) semiconductors such as monolayer MoS 2 and WSe 2 derives in part from their direct optical bandgap and very strong light-matter coupling [1, 2]. In a pristine TMD monolayer, the fundamental optical excitation -the ground-state neutral "A" exciton (X 0 )-can, remarkably, absorb >10% of incoming light [3]. Moreover, in doped or highly excited monolayers distinct resonances due to charged excitons or multiexciton states can develop in optical spectra [4][5][6][7][8][9]. The ability to spectrally resolve these and other features depends critically on material quality, which has markedly improved in recent years as techniques for synthesis, exfoliation, and surface passivation have steadily progressed.The optical quality of exfoliated WS 2 and WSe 2 monolayers has recently improved to the point where signatures of the much weaker excited Rydberg states of X 0 (2s, 2p, 3s, etc.) have been reported based on various linear and nonlinear optical spectroscopies [10][11][12][13][14][15][16]. Correct identification and quantitative measurements of excited excitons are of critical importance in this field, because they provide direct insight into the non-hydrogenic attractive potential between electrons and holes that is believed to exist in 2D materials due to dielectric confinement and nonlocal screening [17][18][19][20][21]. This potential leads, for example, to an unconventionally-spaced Rydberg series of excited excitons and can generate an anomalous ordering of (s, p, d ) levels [10]. Crucially, these excited states allow one to directly estimate the free-particle bandgap and binding energy of the X 0 ground state [10][11][12][13][14][15], both key material parameters that are otherwise difficult to measure in monolayer TMDs, and which are necessarily very sensitive to the surrounding dielectric environment [14,21,22,24]. Greatly desired, therefore, are incisive experimental tools for detailed studies of excited excitons in 2D semiconductors.Historically, optical spectroscopy in high magnetic fields B has provided an especially powerful way to identify and quantify excited excitons [25][26][27][28][29], because each excited state shifts very differently with B. Crucially, these shift...