Considering the abundance of viscoelastic fluids in nature, growing attention has been received for the study of microorganisms in viscoelastic fluids. In Newtonian fluids, the flow of microorganisms is governed by the viscosity alone. But in viscoelastic fluids, the addition of the elastic component complicates the situation. The flow of the organism is now dictated by a combination of the two forces- viscous and elastic. Understanding the behaviour of these organisms is not only important because of the presence of such environments in nature, but also because of the potential pharmaceutical applications that such studies might lead to. This thesis focuses on the experimental study of the swimming of Chlamydomonas reinhardtii, a model motile swimmer that swims at low Reynolds numbers. The main objective of the thesis is to characterize these differences in motility and hydrodynamic interactions of these cells in Newtonian and viscoelastic fluids of varying viscosities. This is accomplished by observing the motion of a dilute suspension of Chlamydomonas reinhardtii in 3D using four cameras. The cells are subsequently tracked using an in-house 3D particle tracking code that incorporates a recursive divide and conquer strategy to reconstruct the trajectories. The experiments showed a drop in velocity in viscoelastic fluids as compared to its Newtonian counterparts, validating the results from existing literature. The cells also maintained their helical motion previously observed in TRIS, although with a drop in radius and pitch in viscoelastic fluids. The ratio of the radius to the pitch, however, remained constant for all the cases, indicating a tendency to retain its overall motion. The study of cell-wall interactions is of prime importance because of the presence of confined surfaces encountered in nature. The concentration profile of the cells was observed to be similar in all the fluids, showing a non-uniform distribution with large concentration at the boundaries. The overall trajectories near the wall in TRIS revealed that the cells tend to arrive at steep angles in the contact region and leave at shallow angles, a phenomenon termed as asymmetric reflection. When the viscosity increased, however, this behaviour became less apparent as the incoming angles became less steep, while the outgoing angles remained shallow. For the viscoelastic case, the behaviour appears to become more symmetric with increase in viscoelasticity. Additionally, the data also points to a less steep drop in velocity in the contact region in solutions of higher viscosity as compared to the less viscous solutions. Though this might indicate a greater influence of hydrodynamics near the wall for more viscous fluids, more data is required to observe this behaviour deeply. The obtained results show a clear effect of viscoelasticity on the motility and kinematics of the cells, confirming results and predictions from existing literature. For cell wall interactions, differences are certainly discerned, not only for the viscoelastic cases but also for the more viscous cases. More experiments on these fluids are recommended to give a clear indication of the change in wall interactions in fluids of higher viscosity and viscoelasticity.