Magnetic fields play a very important role in the dynamics of plasmas. Through interactions with the ions and electrons within plasmas, their behaviour and evolution can be drastically influenced. It is the Zeeman effect that is responsible for the splitting of radiative lines observed. Zeeman spectroscopy is a tool used for the diagnosis of these magnetic fields within plasmas when the extent of this line splitting is observable. Aluminium is chosen as an element to model as it is easy to place within a pinch plasma. It is also relatively easy to ionise Aluminium into being Hydrogen-like within the conditions of pinch plasmas. The calculation of Lyman Alpha and Lyman Beta spectral lineshapes for a Hydrogen-like Aluminium plasma is presented from a fundamental standpoint. The Stark and Zeeman effects are explored and modelled. Modelling of the former is aided by an adapted version of the APEX code by R. Lee in order to calculate the probability distribution of electric fields around a radiator ion in the plasma. Both effects are calculated together as a quantum perturbation to the π = 1, 2, 3 atomic energy levels including fine structure. The lineshapes resulting from this calculation are compared with H-Line’s models (a code also by R. Lee) and shown to be significantly more detailed, including visible Zeeman splitting for test external magnetic fields of B = 100 T and B = 1000 T. Natural and Doppler broadening are also modelled. These extra broadening effects (in particular Doppler) are shown to be destructive to discernable lineshape detail, largely preventing magnetic field diagnosis through Zeeman spectroscopy. Lastly, Lyman Alpha and Lyman Beta are modelled for plasmas with Z-pinch and X-pinch conditions in order to determine the viability of visible Zeeman line splitting.