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\begin{equation}  {\delta g_{\rm HXX} \over g_{\rm HXX}^{\rm SM}} \le 5\% \times \left({1 {\rm TeV} \over \Lambda}\right)^2  \end{equation}   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. In the case of the $Z$ boson, precision measurements at LEP, made with $10^7$ Z decays, were sensitive to weakly-coupled new physics at the TeV scale. An improvement in precision by two orders of magnitude, i.e., an increase in statistics by four orders of magnitude to $> 10^{11}$ $Z$ decays, would be needed to increase this sensitivity up to 10 TeV. Similarly, the current precision of the W and top mass measurements need to be reduced by at least one order of magnitude, i.e., to better than 1 MeV/$c^2$ and 50 MeV/$c^2$ respectively, in order to achieve the same sensitivity.     Among the various proposals 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 between $m_{\rm Z}$ and 500 GeV 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 unprecedented accuracy. This collider is also unique in providing 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 CERN to develop a proposal for an ambitious post-LHC accelerator project at CERN.