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The TOTEM experiment at the LHC has performed the first luminosity-independent determination of the total proton-proton cross-section at . This technique is based on the optical theorem and requires simultaneous measurements of the inelastic rate–accomplished with the forward charged-particle telescopes T1 and T2 in the range 3.1<| η|< 6.5–and of the elastic rate by detecting the outcoming protons with Roman Pot detectors. The data presented here were collected in a dedicated run in 2011 with special beam optics (β*= 90 m) and Roman Pots approaching the beam close enough to register elastic events with squared four-momentum transfers| t| as low as 5· 10 (−)(3) GeV (2). The luminosity-independent results for the elastic, inelastic and total cross-sections are σ (el)=(25.1±1.1) mb, σ (inel)=(72.9±1.5) mb and σ (tot)=(98.0±2.5) mb, respectively. At the same time this method yields the integrated luminosity, in agreement with measurements by CMS. TOTEM has also determined the total cross-section in two complementary ways, both using the CMS luminosity measurement as an input. The first method sums the elastic and inelastic cross-sections and thus does not depend on the ρ parameter. The second applies the optical theorem to the elastic-scattering measurements only and therefore is free of the T1 and T2 measurement uncertainties. The methods, having very different systematic dependences, give results in excellent agreement. Moreover, the ρ-independent measurement makes a first estimate for the ρ parameter at possible:| ρ|= 0.145±0.091.