The goal of this thesis is to use Particle Filters to Simultaneously Localize a mobile robot in an unknown environment and produce an accurate Map. The theory behind Monte Carlo Localization and Occupancy Grid Maps is introduced and compared with improvements to the Particle Filter such as the Shared Gridmaps and Variance Sampler. A Particle Filter algorithm is developed to use sonar measurements to create occupancy maps, and inertial sensors and wheel encoders to update robot's odometry. The Algorithm is applied to a four-wheel robot in an indoor environment with hallways and is successful in creating detailed maps of the test location and accurate estimate of the robot's state.