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\textbf{Abstract}  The discovery by the ATLAS~\cite{v_Aben_Abi_Abolins_et_al__2012} and CMS~\cite{gicevic_Ero_Fabjan_et_al__2012} experiments   of a new boson with mass around 125 GeV/$c^2$ and properties compatible with those of a Standard-Model Higgs boson, coupled with the absence of discoveries of phenomena beyond the Standard Model up to scales of several hundreds GeV, has triggered interest in ideas for future Higgs factories. A new circular $\epem$ collider hosted in a 80- to 100-km tunnel, TLEP, is among the most attractive solutions proposed so far. It has the cleanest experimental environment, produces the highest instantaneous luminosity for top, top-quark,  Higgs boson, W and Z studies, accommodates multiple detectors, and can reach energies all the way to the $\ttbar$ threshold and beyond. It will make possible the measurements of the Higgs boson properties(couplings, width, invisible width, ...)  and of electroweak symmetry-breaking parameters with unequaled precision, offering sensitivity to physics beyond the Standard Model in the multi-TeV range. Moreover, being the natural precursor of a 100-TeV hadron machine in the same tunnel, it offers a long-term vision for particle physics. This paper presents a first appraisal of the salient features of the TLEP physics potential, to serve as a baseline for a more extensive design study.