The TOTEM experiment at the LHC focuses on measuring of the total pp cross-section as well as on studying elastic scattering, diffraction and forward event topologies. The first physics measurement of TOTEM: the measurement of the elastic scattering cross-section using data taken in 2010 will be presented in detail. For the first time after the ISR measurements almost 40 years ago, the t-distribution (-t > 0.4 GeV2) of elastic pp scattering (at ~ 100 times larger energy) has been measured, exhibiting an exponential behavior at smallest |t|-values, followed by a diffractive minimum and subsequently a broad peak, just as at the ISR. The TOTEM measurement confirms the energy dependence of the cross-section behavior indicating an increase of the effective proton radius with increasing energy. In addition, following the successful commissioning of a dedicated LHC optics over the summer, the physics prospects of special runs with this optics in autumn 2011 for a first total cross-section measurement will be discussed.