This is the first of a series of papers in which we present a briefintroduction to the relevant mathematical and physical ideas that form thefoundation of Particle Physics, including Group Theory, Relativistic QuantumMechanics, Quantum Field Theory and Interactions, Abelian and Non-Abelian GaugeTheory, and the SU(3)xSU(2)xU(1) Gauge Theory that describes our universe apartfrom gravity. These notes are not intended to be a comprehensive introductionto any of the ideas contained in them. Among the glaring omissions are CPTtheorems, evaluations of Feynman Diagrams, Renormalization, and Anomalies. Thetopics were chosen according to the authors preferences and agenda. These notesare intended for a student who has completed the standard undergraduate physicsand mathematics courses. Furthermore, these notes should not and will not inany way take the place of the related courses, but rather provide a primer fordetailed courses in QFT, Gauge Theory, String Theory, etc., which will fill inthe many gaps left by this paper.