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Context.Stars form preferentially in clusters embedded inside massive molecular clouds, many of which contain high-mass stars. Thus, a comprehensive understanding of star formation requires a robust and statistically well-constrained characterization of the formation and early evolution of these high-mass star clusters. To achieve this, we designed the ALMAGAL Large Program that observed 1017 high-mass star-forming regions distributed throughout the Galaxy, sampling different evolutionary stages and environmental conditions. Aims.In this work, we present the acquisition and processing of the ALMAGAL data. The main goal is to set up a robust pipeline that generates science-ready products, that is, continuum and spectral cubes for each ALMAGAL field, with a good and uniform quality across the whole sample. Methods.ALMAGAL observations were performed with the Atacama Large Millimeter/submillimeter Array (ALMA). Each field was observed in three different telescope arrays, being sensitive to spatial scales ranging from ≈1000 au up to ≈0.1 pc. The spectral setup allows sensitive (≈0.1 mJy beam⁻¹) imaging of the continuum emission at 219 GHz (or 1.38 mm), and it covers multiple molecular spectral lines observed in four different spectral windows that span about ≈4 GHz in frequency coverage. We have designed a Python-based processing workflow to calibrate and image these observational data. This ALMAGAL pipeline includes an improved continuum determination, suited for line-rich sources; an automatic self-calibration process that reduces phase-noise fluctuations and improves the dynamical range by up to a factor ≈5 in about 15% of the fields; and the combination of data from different telescope arrays to produce science-ready, fully combined images. Results.The final products are a set of uniformly generated continuum images and spectral cubes for each ALMAGAL field, including individual-array and combined-array products. The fully combined products have spatial resolutions in the range 800–2000 au, and mass sensitivities in the range 0.02–0.07M_⊙. We also present a first analysis of the spectral line information included in the ALMAGAL setup, and its potential for future scientific studies. As an example, specific spectral lines (e.g., SiO and CH₃CN) at ≈1000 au scales resolve the presence of multiple outflows in clusters and will help us to search for disk candidates around massive protostars. Moreover, the broad frequency bands provide information on the chemical richness of the different cluster members, which can be used to study the chemical evolution during the formation process of star clusters.