Most of the matter around us today is made up of protons and neutrons, but in the first few moments of the universe the temperature and density were too high for tightly bound protons and neutrons to form. Instead of being bound inside protons and neutrons, quarks and gluons existed in a plasma-like fluid called the Quark Gluon Plasma (QGP). As the universe cooled and expanded, the matter that we have today began to form. An understanding of nuclear matter and the transition from QGP to normal matter (and vice versa) can in principle be ascertained from the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). In practice though, the current state-of-the-art calculations provide only limited information about the properties of QCD matter. The transition from normal matter to QGP can be studied in the laboratory using relativistic heavy-ion collisions like those produced by the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory.

Studying the QGP through heavy-ion collisions has its challenges though, since the created matter evolves through many stages before the final state particles can be detected. Learning about the earliest stages of the system requires penetrating probes, capable of carrying information from inside the medium out to the final state. Electromagnetic probes, such as leptons, are inert to the strong force. For this reason, they carry pristine information from all stages of the created medium. Dileptons (l+l-) are even more valuable, since the various production mechanisms and time periods of the system can be distinguished through the invariant mass of the pair. For instance, the suppression in production of heavy quark (charm and bottom) bound states, which can be identified through dileptons, has long been considered a direct probe of the QGP. At lower masses dileptons can be used to measure the spectrum of thermal radiation of the medium, acting as a "fireball thermometer". Dileptons are also linked to the phenomena of spontaneous chiral symmetry breaking (and its expected restoration inside the QGP) through the rho-meson which decays into dileptons.

In this thesis, the first measurements of the dilepton invariant mass spectra through the dimuon (mu+mu-) channel with the Solenoidal Tracker at RHIC (STAR) are presented. The mu+mu- invariant mass spectra is measured in data from p+p collisions at sqrt(s) = 200 GeV and p+Au collisions at sqrt(sNN) = 200 GeV. The first measurement of the phi -> mu+mu- spectra at STAR is also measured in p+p collisions at sqrt(s) = 200 GeV. For these analyses novel muon identification techniques were developed to combat the contamination from hadrons and secondary muons resulting from weak decays. Techniques are presented for training and employing deep neural networks for the identification of muons and for the rejection of backgrounds. Data-driven techniques are presented for the measurement of muon-purity and for the estimation of physical backgrounds to the mu+mu- invariant mass spectra. The measurement of the mu+mu- invariant mass spectra in p+p and p+Au collisions is also compared with the expected dimuon yields from light hadron decays, open heavy flavor decays, and the Drell-Yan process. Finally, the potential for future dilepton measurements at STAR is discussed in light of the new datasets collected in the recent years.