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 GeV2. The luminosity-independent results for the elastic, inelastic and total cross-sections are σel = (25.1 ± 1.1) mb, σinel = (72.9 ± 1.5) mb and σtot = (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.