The restart of the Large Hadron Collider (LHC) at CERN, foreseen in November 2009 after the incident of 2008, will finally open a new window on the physics at the TeV scale and will allow the discovery of the Standard Model Higgs boson, if it exists, or of possible alternative schemes for the spontaneous symmetry-breaking mechanism. Moreover the LHC Collider will hopefully provide an answer to one of the most compelling questions of today coming from astronomical observations, astrophysics and cosmic ray experiments: which is the particle physics candidate for the Dark Matter component of the Universe? Supersymmetry (SUSY) is a theoretically attractive scenario for physics beyond the Standard Model which can provide a suitable Dark Matter candidate in case R-parity is conserved. If SUSY is manifesting at the TeV scale, as favored by several arguments, it will be accessible at the LHC Collider within the first few years of data taking. In this paper search strategies for a generic SUSY models with R-parity conservation with the ATLAS detector are described. These inclusive search strategies are based on signatures with missing transverse momentum from undetected neutralinos, in addition to multiple hard jets and leptons. The corresponding discovery reach for the first fb −1 of integrated luminosity of ATLAS data will be presented together with a discussion of possible measurements needed to extract the masses of SUSY particles including the Lightest Supersymmetric Particle (LSP), which in various supersymmetric (SUSY) symmetry breaking scenarios, is the lightest neutralino χ ˜ 1 0 .