Stellar surfaces have been directly observed in primarily two limits of resolution. One provides a wealth of intricate observables and overwhelming detail in the case of our own Sun (Galilei 1613), equaled in measure by the difficulty to model such complex behavior. The other extreme provides scarce inferred detail (Gilliland & Dupree 1996) to simply none at all, for nearly every other star in the Universe. Transit mapping is a technique allowing for high–resolution analysis of surface inhomogeneities on active stars (those on the lower main sequence with convective envelopes) by using the system’s planetary components as the surface probe.

Observation from the ground is a daunting task. The necessary high precision photometry required to unambiguously identify and constrain stellar surface features is challenging because of atmospheric distortion and periodic coverage gaps due to Earth’s rotation. To achieve the required precision for this technique to work effectively, it is necessary to take data from space, outside of the influence of Earth’s atmosphere and rotation. The primary objective of the NASA Kepler spacecraft is to search for planets via the transit method (Borucki et al. 2010), such that its sensitivity towards the detection of these objects and its capability to collect long stretches of uninterrupted coverage makes Kepler the idea instrument for analysis of time evolving surface features using transit mapping.

In this thesis I use data taken by the Kepler spacecraft to model the spatial and temporal starspot coverage for HAT–P–11 (Kepler–3), a bright K4 dwarf in the Kepler field. The precision allowed by Kepler provides an opportunity to model stellar surfaces both in and out–of–transit, a unique ability unmatched by any other instrument or technique. In addition to having an activity map of the stellar surface, this study addresses correlations between stellar properties, starspot size and frequency, spot motion from rotation to rotation, and overall spot coverage.