Protostellar jets are an important component of star formation, acting as a window into the inner regions of the protoplanetary disk while also impacting on the evolution of the star-disk system and the surrounding molecular cloud. Integral field spectroscopy (IFS) has proven a valuable tool for jet studies, as this allows three-dimensional spa- tial and spectral information to be collected simultaneously across the extended jet. VLT/MUSE is an exceptionally powerful IFS instrument operating in the optical and near-infrared (NIR) band with large spatial and spectral coverage. In this thesis, we present the analysis of MUSE observations of the jet from the Classical T Tauri Star Th 28 to explore the potential of MUSE for jet studies and to develop Python tools which support the analysis of MUSE data. We are able to characterise the morphology and kinematics of the Th 28 jet in detail, including six newly identified knots. A key result from our analysis of the jet morphology is the detection of a ‘wiggling’ in the jet which shows a clear point-symmetry between the jet lobes indicating precession. We model the jet trajectory and show that this may be the signature of a brown dwarf compan- ion (≤ 70 MJup) orbiting within the inner disk region. This work also investigates the physical diagnostics of the jet using optical and NIR emission line ratios, and highlights the asymmetric densities and excitation conditions between the two lobes of the jet, in tandem with their asymmetric morphologies and velocities. The results of this project to date emphasize both the potential for further work investigating the origins of the ob- served asymmetries and precession in the Th 28 jet, and the incredible power of MUSE to comprehensively investigate protostellar jets.