Richard Lebed's research involves studying the properties of, and interactions between, particles at the most elementary level. One of the most fruitful ideas in the history of particle physics has been the recognition that beautiful symmetries interlace the fabric of physical theories, and not only tell us a great deal about how particles interact, but even restrict the types of particles that can exist. He has worked in a number of theoretical subfields of particle physics, for example: i) What if the structure of spacetime is not smooth, but rather coordinate operators fail to commute, just like x and px in quantum mechanics? How can we tell? ii) Why is there a three-fold replication of fermions in the Standard Model? For example, the muon appears to be just a heavy replica of the electron. If we build a symmetry that explains this redundancy, what does it imply about neutrino masses and mixing? iii) The theory of strong interactions, QCD, has three color charges. What if this number were different? How would properties like the mass of protons and neutrons change? iv) Why has it taken so long to discover ``exotic'' strongly interacting particles that are bound states in categories other than triples of quarks (like protons and neutrons) or quark-antiquark pairs (like pions), and how are these exotics assembled?