IGR J17591-2342 is a recently INTEGRAL discovered accreting millisecond X-ray pulsar that went into outburst around July 21, 2018. To better understand the physics acting in these systems during the outburst episode we performed detailed temporal-, timing- and spectral analyses across the 0.3-300 keV band using data from NICER, XMM-Newton, NuSTAR and INTEGRAL. The hard X-ray 20-60 keV outburst profile is composed of four flares. During the maximum of the last flare we discovered a type-I thermonuclear burst in INTEGRAL JEM-X data. We derived a distance of 7.6+/-0.7 kpc, adopting Eddington luminosity limited photospheric radius expansion burst emission and assuming anisotropic emission. In the timing analysis using all NICER 1-10 keV monitoring data we observed a rather complex behaviour starting with a spin-up period, followed by a frequency drop, a episode of constant frequency and concluding with irregular behaviour till the end of the outburst. The 1-50 keV phase distributions of the pulsed emission, detected up to $sim$ 120 keV using INTEGRAL ISGRI data, was decomposed in three Fourier harmonics showing that the pulsed fraction of the fundamental increases from ~10% to ~17% going from ~1.5 to ~4 keV, while the harder photons arrive earlier than the soft photons for energies <10 keV. The total emission spectrum of IGR J17591-2342 across the 0.3-150 keV band could adequately be fitted in terms of an absorbed compPS model yielding as best fit parameters a column density of N_H=(2.09+/-0.05) x 10^{22} /cm2, a blackbody seed photon temperature kT_bb,seed of 0.64+/- 0.02 keV, electron temperature kT_e=38.8+/-1.2 keV and Thomson optical depth Tau_T=1.59+/-0.04. The fit normalisation results in an emission area radius of 11.3+/-0.5 km adopting a distance of 7.6 kpc. Finally, the results are discussed within the framework of accretion physics- and X-ray thermonuclear burst theory.
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