  In this Ph.D. thesis, the primary goal is to present a recent investigation
of the finite density thermodynamics of hot and dense quark-gluon plasma. As we
are interested in a temperature regime, in which naive perturbation theory is
known 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 employ
two different frameworks. We first use hard-thermal-loop perturbation theory
(HLTpt) at leading order to obtain the pressure for nonvanishing quark chemical
potentials, and next, inspired by dimensional reduction, resum the known
four-loop weak coupling expansion for the quantity.
  We present and analyze our findings for various cumulants of conserved
charges. This provides us with information, through correlations and
fluctuations, on the degrees of freedom effectively present in the quark-gluon
plasma right above the deconfinement transition. Moreover, we compare our
results with state-of-the-art lattice Monte Carlo simulations as well as with a
recent three-loop mass truncated HTLpt calculation. We obtain very good
agreement between the two different perturbative schemes, as well as between
them and lattice data, down to surprisingly low temperatures right above the
phase transition. We also quantitatively test the convergence of an
approximation, which is used in higher order loop calculations in HTLpt. This
method based on expansions in mass parameters, is unavoidable beyond leading
order, thus motivating our investigation. We find the ensuing convergence to be
very fast, validating its use in higher order computations.
