"Vigorous experimental and theoretical programs are underway to study the behaviour of strongly interacting systems in extreme conditions of temperature and density. The only practical way to create such systems in terrestrial laboratories is to collide nuclei at relativistic energies. This is done at accelerator facilities such as the LHC (CERN, Geneva) and RHIC (Brookhaven National Laboratory, USA). These collisions of heavy ions contain so much energy in such a small volume that the colliding nuclei "melt" into a plasma of quarks and gluons. This creates an exotic form of nuclear matter: the quark-gluon plasma (QGP), which exists but for a fleeting moment, and can be studied through the particles that stream to the detectors. Two such particles are leptons and photons, which this research will focus on. As it was discovered that the QGP can be very well modelled by relativistic fluid dynamics, there has been a large theoretical effort to completely characterize this QGP and understand its bulk properties. One of the aims of the McGill group is to obtain a value for the shear and bulk viscosities of the plasma: those are transport coefficients linked to fundamental properties of quantum chromodynamics (QCD), the theory of the nuclear strong interaction. The production of photons and dileptons can be used as probes to study these transport coefficients as they are emitted throughout the out-of-equilibrium evolution of the QGP medium, as well as within thermal equilibrium. In order for such studies to be done, the electromagnetic signal from the pre-equilibrium phase needs to be quantified, which is the topic of this thesis. Using kinetic theory, the production rate of dileptons and photons was calculated for both thermal equilibrium and pre-equilibrium cases. In the thermal equilibrium case, results of the numerical integration of the differential dilepton and photon production rates were matched to the analytical solution. For the out-of-equilibrium case, transport equations derived within the diffusion approximation of the Boltzmann equation were solved numerically to study the thermalization of quarks and gluons in quark-gluon plasma." --