The fundamentals of Geometric Algebra (Clifford algebras) will be presented alongside some basic applications in physics. Namely, the geometric algebras of 2-dimensional space, 3-dimensional space, and (1,3)- dimensional space will be briefly shown. Within the 3-dimensional geometric algebra, a relatively unknown physical approach, wherein Lorentz transformations can be used to derive equations of motion, will be demonstrated. Thereafter will the potential usefulness of Projective Geometric Algebra be shown by its allowing for coordinate free physics, dimension-agnostic physics, and the mathematical unification of translation and rotation. The generalization of the derivative within the framework of Geometric Algebra will be presented, and the Euler-Lagrange equation within this framework will be derived. Finally, current and potential research areas will be discussed in the realm of Projective Geometric Algebra and Field Theory.