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The science of ultra-high energy cosmic rays after more than 15 years of operation of the Pierre Auger Observatory

. The Pierre Auger Observatory has been detecting ultra-high energy cosmic rays (UHECRs) for more than ﬁfteen years. An essential feature of the Observatory is its hybrid design: cosmic rays above 100 PeV are detected through the observation of the associated air showers with diﬀerent and complementary techniques, from surface detector arrays and ﬂuorescence telescopes to radio antennas. The analyses of the multi-detector data have enabled high-statistics and high-precision studies of the energy spectrum, mass composition and distribution of arrival directions of UHECRs. The resulting picture is summarized in this contribution. While no discrete source of UHECRs has been identiﬁed so far, the extragalactic origin of the particles has been recently determined from the arrival directions above 8 EeV, and the ring is closing around nearby astrophysical sites at higher energies. Also, the established upper limits on ﬂuxes of UHE neutrinos and photons have implications on dark matter and cosmological aspects that are also presented in this contribution.