Abstract: This thesis is devoted to the expansion of the technique of electron reflectometry from its prior purpose in mapping lunar crustal magnetic fields to the same purpose at Mars, where the presence of a substantial atmosphere considerably complicates matters. Previous work, using magnetometer data from the Mars Global Surveyor (MGS) spacecraft, established the existence of surprisingly strong crustal remanent magnetic fields and placed important constraints both upon the properties of the crustal magnetic sources responsible for the fields and upon the timing and orientation of Mars's ancient core dynamo. To build upon this work, I have analyzed pitch angle distributions of magnetically reflecting solar wind electrons measured by the MGS Magnetometer/Electron Reflectometer (MAG/ER) to create a map of Martian crustal magnetic fields at ∼195 km altitude, giving greater spatial resolution and sensitivity than was previously possible using magnetometer data alone. Low magnetic fields measured above most volcanoes indicate thermal demagnetization of the crust by magmatism and underplating after the cessation of the core dynamo, while relatively high fields measured above the Hadriaca Patera volcano imply that Martian volcanism predates this cessation and is significantly older than any exposed volcanic surface. The geographic and size distribution of demagnetization signatures of impact craters and the suggested presence of magnetic edge effects, indicates that (1) crustal magnetization occurs at typically shallower depths in the northern Martian lowlands than in the southern highlands and (2) the typical crustal magnetic coherence scale, is >100 km. A comparison of crater retention ages with magnetic signatures of some of the oldest impact basins on Mars confirms that Mars's core dynamo ceased operating early in the planet's history, >4 billion years ago. Significant differences in magnetization between geologically contemporary basins suggests that the dynamo's final weakening and death may have taken place over as little as 10-30 million years. An unintended benefit of this analysis has been a modification of the ER technique to produce measurements of mass densities in the Martian upper thermosphere (∼200 km), which show that variations in extreme ultraviolet flux likely affect interannual variability of these densities, particularly near aphelion and that the effects of global lower atmospheric dust storms do not appear to propagate to these altitudes.