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Rare kaon decay measurements at CERN are listed as an essential scientific activity in the 2020 Update of the European strategy for particle physics. The High Intensity Kaon Experiments (HIKE) represent a broad, long-term next-generation fixed-target experimental programme at CERN after LS3 , based in the North Area ECN3 experimental hall, covering all the main aspects of rare kaon decays and searches accessible via kaon physics, from ultra-rare kaon decays to precision measurements and searches for new phenomena, with unprecedented world-leading sensitivity. HIKE will also perform tests of SM cornerstone principles like lepton number and flavour universalities, with unparallel sensitivity. Building on the CERN long-standing experience in kaon experiments (NA31, NA48 , NA62), the HIKE program overall has a great potential for discovery and consequently for characterising and testing the New Physics flavour structure. HIKE will profit from a beam intensity increase by a factor between four and six with respect to the NA62 experiment, and cutting-edge detector technologies. For HIKE , new or upgraded detectors will replace those of NA62 with the goal of sustaining secondary-beam rates four times higher to boost the statistical sensitivity. To this end, new technologies will be used, in synergy with the upgrades of the LHC experiments. The proposed HIKE program consists of multiple phases and includes both a charged beam (𝐾+) phase and a neutral beam (𝐾𝐿) phase, as well as periods in beam dump mode. The long decay volume and detector characteristics needed for kaon physics make HIKE suitable to search for new feebly-interacting, long-lived particles, providing unique sensitivity to forward processes. All phases of the HIKE programme will use shared detectors and infrastructure. The detector design is challenging but at least one technological solution exists for each subsystem, thanks also to the synergy with HL-LHC. The various phases allow for insertion, repositioning, or removal of specific detector elements depending on the physics requirements, while the overall setup remains broadly the same.