In this paper we introduce the MOBSTER collaboration and lay out its scientific goals. We present first results based on the analysis of nineteen previously known magnetic O, B and A stars observed in 2-minute cadence in sectors 1 and 2 of the Transiting Exoplanet Survey Satellite (TESS) mission. We derive precise rotational periods from the newly obtained light curves and compare them to previously published values. We also discuss the overall photometric phenomenology of the known magnetic massive and intermediate-mass stars and propose an observational strategy to augment this population by taking advantage of the high-quality observations produced by TESS.
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