Researchers at CERN (European Organization for Nuclear Research) near Geneva have started to seriously discuss the need for a new large accelerator for future generations of particle physicists. The most likely scenario seems to be a collider built in the Geneva area with a circumference of 80 or 100 km in which protons would collide (as is the case of the existing Large Hadron Collider at CERN). Other options are also being considered, such as the electron-positron collider which would precede the proton machine or electron-proton collider. The main scientific motivation is to find signals of new physics (i.e. those not predicted by the Standard Model of elementary particles) and/or to measure properties of the recently discovered Higgs boson with much higher precision than that foreseen to be achieved by the end of LHC in about 20 years. A sufficiently fast development of various technologies is the key to this new powerful accelerator. For the proton machine, the main components are magnets with high magnetic field that are expected to be built based on high-temperature superconducting materials, while the lepton machine needs a new generation of accelerating cavities with a high gradient of electric field, high power transfer efficiency and high reliability., Marek Taševský., and Obsahuje seznam literatury