In this thesis we explore the effects of chemical potentials or charge densities inside a thermal plasma,
which is governed by a strongly coupled gauge theory. Since perturbative methods in general fail in this regime,
we make use of the AdS/CFT correspondence which originates from string theory. AdS/CFT is a gauge/gravity
duality (also called holography), which we utilize here to translate perturbative gravity calculations into
results in a gauge theory at strong coupling. As a model theory for Quantum-Chromo-Dynamics (QCD),
we investigate N=4 Super-Yang-Mills theory in four space-time dimensions. This theory is coupled to
fundamental hypermultiplets of N=2 Super-Yang-Mills theory. In spite of being quite different from QCD
this model succeeds in describing many of the phenomena qualitatively, which are present in the strong interaction.
Thus, the effects discovered in this thesis may also be taken as predictions for heavy ion collisions at the
RHIC collider in Brookhaven or the LHC in Geneva. In particular we successively study the introduction
of baryon charge, isospin charge and finally both charges (or chemical potentials) simultaneously.

We examine the thermodynamics of the strongly coupled plasma. Phase diagrams are given for the
canonical and grandcanonical ensemble. Furthermore, we compute the most important thermodynamical
quantities as functions of temperature and charge densities~(or chemical potentials): the free energy, grandcanonical
potential, internal energy and entropy. Narrow resonances which we observe in the flavor current spectral functions
follow the (holographically found) vector meson mass formula at low temperature. Increasing the
temperature the meson masses first decrease in order to turn around at some temperature and
then increase as the high-temperature regime is entered. While the narrow resonances at low temperatures can be
interpreted as stable mesonic quasi-particles, the resonances in the high-temperature regime are
very broad. We discuss these two different temperature-regimes
and the physical relevance of the discovered turning point that connects them. Moreover, we find that flavor currents
with isospin structure in a plasma at finite isospin density show a triplet splitting of the resonances in the
spectral functions. Our analytical calculations confirm this triplet splitting also for the diffusion pole, which is
holographically identified with the lowest lying quasinormal frequency. We discuss the non-vanishing
quark condensate. Furthermore, the baryon diffusion coefficient depends non-trivially on both: baryon
and isospin density. Guided by discontinuities in the condensate and densities, we discover a phase transition
resembling the one found in the case of 2-flavor QCD. Finally, we extend our hydrodynamic considerations
to the diffusion of charmonium at weak and strong coupling. As expected, the ratio of the
diffusion coefficient to the meson mass shift at strong coupling is significantly smaller than
the weak coupling result. This result is reminiscent of the result for the viscosity to entropy density ratio,
which is significantly smaller at strong coupling compared to its value at weak coupling.