  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.
