Resummed Thermodynamics at Finite Temperature and Density

I will present the result of a calculation of the finite temperature thermodynamic functions of a quark-gluon plasma for general $N_c$ and $N_f$ to three-loop order using hard-thermal-loop perturbation theory. At this order, all ultraviolet divergences can be absorbed into renormalizations of the vacuum energy, the HTL mass parameters, and the strong coupling constant. I will show that at three loops, the results for the pressure, energy density, entropy density, and the trace anomaly are in very good agreement with lattice data down to temperatures $T > 2\,T_c$. In addition, I will present results of a recent two-loop calculation at finite temperature and chemical potential utilizing the same framework.