AU Mic is a young, active star whose transiting planet was recently detected. We report our analysis of its TESS data, where we modeled the BY Draconis type quasi-periodic rotational modulation by starspots simultaneously to the flaring activity and planetary transits. We measured a flare occurrence rate of 6.35 flares per day for flares with amplitudes in the range of $0.06% < f_{rm max} < 1.5%$ of the star flux. We employed a Bayesian MCMC analysis to model the five transits of AU Mic b, improving the constraints on the planetary parameters. The planet radius of $4.07pm0.17$~R$_{oplus}$ and a mean density of $1.4pm0.4$~g~cm$^{-3}$ confirms that it is a Neptune-size moderately inflated planet. While a single feature possibly due to a second planet was previously reported in the former TESS data, we report the detection of two additional transit-like events in the new TESS observations of July 2020. This represents substantial evidence for a second planet (AU Mic c) in the system. We analyzed its three transits and obtained an orbital period of $18.859019pm0.000016$~d and a planetary radius of $3.24pm0.16$~R$_{oplus}$, which defines it as a warm Neptune-size planet with an expected mass in the range of 2.2~M$_{oplus}$~$< M_{rm c} < $25.0~M$_{oplus}$. The two planets in the system are in near 9:4 mean-motion resonance. We show that this configuration is dynamically stable and should produce transit-timing variations (TTV). Our non-detection of significant TTV in AU Mic b suggests an upper limit for the mass of AU Mic c of $<7$~M$_{oplus}$, indicating that this planet is also likely to be inflated. As a young multi-planet system with at least two transiting planets, AU Mic becomes a key system for the study of atmospheres of infant planets and of planet-planet and planet-disk dynamics at the early stages of planetary evolution.
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