Just like light waves, gravitational waves are most generally characterized by their propagation direction and time-dependent waveform in each of two independent polarization states. These properties of incident gravitational plane waves can be inferred from observations made in a properly oriented network of detectors. You will learn to characterize the wave polarization via its (frequency dependent) Stokes parameters to infer important, general properties of the wave's source: e.g., point sources of circularly polarized radiation must be non-axisymmetric and radiating angular momentum, while point sources of linearly polarized waves must be either axisymmetric or oriented so that the direction of angular momentum loss is orthogonal to the observer line-of-sight. This is particularly interesting for more exotic sources, e.g., black hole binaries with high spin or high eccentricity. You will find the regions of the gravitational wave sky where the LIGO-Virgo network is sensitive to both gravitational wave polarizations, and estimate the number of sources.
The first event where both polarizations were detected is GW170814. You will start by computing the Stokes parameters for this event.