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Therefore the Higgs boson couplings need to be measured with a per-cent accuracy or better to be sensitive to 1~TeV new physics, and with a per-mil accuracy to be sensitive to multi-TeV new physics. Similarly, Electroweak precision measurements made at LEP with $10^7$ Z decays, together with accurate W and top-quark mass measurements from the Tevatron, are sensitive to weakly-coupled new physics at the TeV scale. To increase this sensitivity up to 10~TeV, an improvement in precision by two orders of magnitude, i.e., an increase in statistics by four orders of magnitude to at least $10^{11}$ Z decays, would be needed. At the same time, the current precision of the W and top-quark mass measurements needs to be improved by at least one order of magnitude, i.e., to better than 1~MeV and 50~MeV respectively, in order to match the increased Z-pole measurement sensitivity. These experimental endeavours will also require significant theoretical effort in a new generation of theoretical calculations in order to reap the full benefits from their interpretation.  Among the various possibilities on the table today (pp colliders, $\epem$ colliders, $\mu^+\mu^-$ colliders and $\gamma\gamma$ colliders), it seems that only circular $\epem$ colliders can deliver the integrated luminosities that would be adequate to reach such levels of precision. The proposed TLEP $\epem$ collider~\cite{cite:1305.6498}, which could be hosted in a new 80 to 100 km tunnel~\cite{cite:Osborne} in the Geneva area, as seen in Fig.~\ref{fig:TLEP80}, would be able to produce collisions at centre-of-mass energies from 90 to 350~GeV and beyond beyond,  at several interaction points, and make precision measurements at the Z pole, at the WW threshold, at the HZ cross section maximum, and at the $\ttbar$ threshold, with an unequalled accuracy. This collider also provides a possible upgrade to a hadron collider (called the VHE-LHC) in the same tunnel, at a centre-of-mass energy of up to 100~TeV, which would give direct access to new physics up to scales of 10~TeV or more. This vision is fully in-line with the recent update of the European Strategy, approved at the end of May 2013 by the CERN Council~\cite{cite:Strategy}, which calls upon the Organization to develop a proposal for an ambitious post-LHC accelerator project at CERN.