  Enabled by the addition of a TOF detector system in 2010, the first phase of
the Beam Energy Scan (BES-I) at RHIC allows STAR to conduct an unprecedented
energy-dependent study of dielectron production within a homogeneous
experimental environment, and hence close the wide gap in the QCD phase diagram
between SPS and top RHIC energies. This thesis concentrates on the
understanding of the LMR enhancement regarding its $M_{ee}$, $p_{T}$ and energy
dependence. It studies dielectron production in Au+Au collisions at beam
energies of 19.6, 27, 39, and 62.4 GeV with sufficient statistics. In
conjunction with the published STAR results at top RHIC energy, this thesis
presents results on the first comprehensive energy-dependent study of
dielectron production.
  The comparison of $M_{ee}$- and $p_{T}$-spectra with cocktail simulations of
hadronic sources reveals a sizeable and steadily increasing excess yield in the
LMR at all beam energies. The scenario of broadened in-medium $\rho$ spectral
functions proves to not only serve well as dominating underlying source but
also to be universal in nature since it quantitatively and qualitatively
explains the LMR enhancements from SPS to top RHIC energies. It shows that most
of the enhancement is governed by interactions of the $\rho$ meson with thermal
resonance excitations in the late(r)-stage hot and dense hadronic phase. This
conclusion is supported by the energy-dependent measurement of integrated LMR
excess yields and enhancement factors. The former do not exhibit a strong
dependence on beam energy as expected from the approximately constant total
baryon density above 20 GeV, and the latter show agreement with the CERES
measurement at SPS energy. The consistency in excess yields and agreement with
model calculations over the wide RHIC energy regime makes a strong case for LMR
enhancements on the order of a factor 2-3.
