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In this Ph.D. thesis, the primary goal is to present a recent investigationof the finite density thermodynamics of hot and dense quark-gluon plasma. As weare interested in a temperature regime, in which naive perturbation theory isknown to lose its predictive power, we clearly need to use a refined approach.To this end, we adopt a resummed perturbation theory point of view and employtwo different frameworks. We first use hard-thermal-loop perturbation theory(HLTpt) at leading order to obtain the pressure for nonvanishing quark chemicalpotentials, and next, inspired by dimensional reduction, resum the knownfour-loop weak coupling expansion for the quantity.  We present and analyze our findings for various cumulants of conservedcharges. This provides us with information, through correlations andfluctuations, on the degrees of freedom effectively present in the quark-gluonplasma right above the deconfinement transition. Moreover, we compare ourresults with state-of-the-art lattice Monte Carlo simulations as well as with arecent three-loop mass truncated HTLpt calculation. We obtain very goodagreement between the two different perturbative schemes, as well as betweenthem and lattice data, down to surprisingly low temperatures right above thephase transition. We also quantitatively test the convergence of anapproximation, which is used in higher order loop calculations in HTLpt. Thismethod based on expansions in mass parameters, is unavoidable beyond leadingorder, thus motivating our investigation. We find the ensuing convergence to bevery fast, validating its use in higher order computations.

Probing the finite density equation of state of QCD via resummed perturbation theory