AU Microscopii (AU Mic) is a young, active star whose transiting planet was recently detected. Here, we report our analysis of its TESS light curve, 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 in AU Mic of 6.35 flares per day for flares with amplitudes in the range of 0.06% < f_max < 1.5% of the star flux. We employed a Bayesian Markov chain Monte Carlo analysis to model the five transits of AU Mic b observed by TESS, improving the constraints on the planetary parameters. The measured planet-to-star effective radius ratio of R_p∕R_⋆ = 0.0496 ± 0.0007 implies a physical radius of 4.07 ± 0.17 R_⊕ and a planet density of 1.4 ± 0.4 g cm⁻³, confirming that AU Mic b 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 available transits and obtained an orbital period of 18.859019 ± 0.000016 d and a planetary radius of 3.24 ± 0.16 R_⊕, which defines AU Mic c as a warm Neptune-size planet with an expected mass in the range of 2.2 M_⊕ < M_c < 25.0 M_⊕, estimated from the population of exoplanets of similar sizes. The two planets in the AU Mic 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_⊕, 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.