We live in a golden era of exoplanet discovery and characterization. Since its launch in 2009, the Kepler Mission has discovered over 4000 exoplanets, enabling detailed studies of their physical and orbital properties. These include empirical studies of the prevalence of planets of various sizes and orbital distances. In some of the Kepler systems, the compositions of the planets have been determined. Other studies include empirical, analytical, and numerical constraints on the formation and evolution of planetary systems.

This thesis focuses on two aspects of the Kepler revolution. The first focus is on the masses and densities of small planets. Planets smaller than Neptune span a variety of compositions. Some of them are rocky and potentially habitable. The diversity of compositions among sub-Neptunes offers clues to planet formation and evolution. To determine the compositions of small planets, it is necessary to compute bulk densities from measurements of the planet radii and masses. While Kepler has determined the radii of thousands of planets, only a handful of the small planets are amenable to mass measurement techniques. Using the results from two mass measurement techniques, called the radial velocity (or Doppler) method and the transit timing variation method, a detailed study of the masses and compositions of more than 65 small planets was conducted. This study determined empirical relationships that describe the average masses and densities of exoplanets smaller than Neptune as a function of planet radius. Such exoplanets achieve a peak bulk density of 7.6 grams per cubic centimeter at a physical size of 1.5 times the radius of Earth. This peak density corresponds to a rocky composition; rocky planets smaller than 1.5 Earth radii are less compressed and less dense, whereas planets larger than 1.5 Earth radii have thick envelopes composed of volatile gases that lower their bulk densities.

The second focus of this thesis is on the masses and orbital dynamics of planets in multi- planet systems. Multi-planet systems represent the end-states of planet formation. Their orbital dynamics and planet compositions are a fossil record of how they arrived at their present configurations. The systems studied herein include 3 multi-planet systems: KOI- 94, Kepler-10, and Kepler-11. KOI-94 is a system of 4 planets including a warm Jovian world. Kepler-10 contains a scorched rocky planet, a cooler gas-enveloped world, and a likely third planet. Kepler-11 has six small planets with fluffy hydrogen-rich envelopes, all contained within the equivalent orbital distance of Venus. Measurements of the compositions and orbital dynamics of these planets offer valuable steps toward characterizing the possible formation and evolutionary histories of these planetary systems.