Abstract: The fractional quantum Hall effect (FQHE) occurs when a two-dimensional electron gas (2DEG) is subjected to a large perpendicular magnetic field at low temperatures. At certain magnetic field values determined by the density of the electron gas, the system forms highly correlated ground states with a gap to low-lying excitations. In these states, the transverse Hall resistance is quantized to rational fractions of h/e2 and the longitudinal resistance vanishes. Remarkably, theory predicts that the excitations of the FQHE carry fractional charge and fractional statistics, possibly even non-Abelian statistics in certain cases. The search for “topological” materials with fractional charge and unusual statistics is currently an exciting branch of condensed matter physics spanning many different physical systems. Here I will describe how we create extremely high quality 2DEGs in AlGaAs/GaAs heterostructures using molecular beam epitaxy and the basics of electron transport experiments we use to study them. Building on this knowledge, I will discuss how we currently attempt to probe statistics in the FQHE via Aharonov-Bohm interference in small electronic Fabry-Perot interferometers. We have recently demonstrated highly coherent Aharonov-Bohm oscillations in the fractional quantum Hall regime. This result indicates we may have a viable platform for measurement of particle statistics in a condensed matter system.