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We present the Colombo-Argentinian Muography Program for studying inland Latin-American volcanoes. It describes the implementation of a simulation framework covering various factors with different spatial and time scales: the geomagnetic effects at a particular geographic point, the development of extensive air showers in the atmosphere, the propagation through the scanned structure and the detector response. Next, we sketch the criteria adopted for designing, building, and commissioning MuTe: a hybrid Muon Telescope based on a composite detection technique. It combines a hodoscope for particle tracking and a water Cherenkov detector to enhance the muon-to-background-signal separation due to extensive air showers' soft and multiple-particle components. MuTe also discriminates inverse-trajectory and lowmomentum muons by using a picosecond Time-of-Flight system. We also characterise the instrument's structural -mechanical and thermal-behaviour, discussing preliminary results from the background composition and the telescope-health monitoring variables. Finally, we discuss the implementations of an optimisation algorithm to improve the volcano internal density distribution estimation and machine learning techniques for background rejection.