Precision measurements on low energy atomic systems are powerful tools for testing our understanding of the fundamental laws of the universe. Work on two complementary projects dedicated towards Matter-antimatter, Lorentz Symmetry tests (MAMLS) , and searches for new exotic physics is proposed. One project seeks a precise measurement of the proton, and eventually antiproton, magnetic moment using a Penning trap located at the Johannes Gutenberg Universität Mainz. The apparatus will be upgraded to allow for an accurate measurement of the proton magnetic moment at the part per billion level. The experimental techniques developed during this project will be directly applicable to a parallel project that is currently under construction by a collaborating group with the goal of measuring the antiproton magnetic moment. Comparison of the proton and antiproton magnetic moments will constitute a new test of matter-antimatter symmetry for baryonic systems. The other component of the project involves the development of experimental searches for new physics using atomic systems. The work will focus on the feasibility of using an optical magnetometer network to detect possible dark matter candidates and using atomic clocks and parity violation experiments to place more stringent bounds of violation of Lorentz invariance.