This chapter explores fundamental concepts underpinning the geometry of Minkowski spacetime. The discussion begins with a short review of Special Relativity and the notion of tensors and their transformations under the Lorentz group. Representations of the Lorentz group are then built, finite-dimensional representations with their link with SU(2) and infinite-dimensional representations. Spin representations allow for the introduction of Dirac spinors and their interaction with spacetime symmetries in the Minkowski manifold. The discussion is pursued through the construction of Lorentz scalars from Dirac spinors, examining their transformation properties under Lorentz transformations. It establishes the Dirac conjugate and Lorentz vector properties, culminating in a comprehensive exploration of Dirac, Weyl, and Majorana fermions. Key topics include the formulation of the Dirac equation, distinctions between fermion types, and implications for quantum field theory. The chapter concludes by outlining the development of a single-particle wave equation for photons, drawing parallels with Dirac’s formulation for spin-1/2 particles.