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Dirac Equation

Interesting notes from this post by Lubos Motl

However, the Dirac equation leads to many conclusions and extensions that will are going to discuss in some detail:

need to second-quantize the Dirac field; antiparticles; quantum field theory;
non-Abelian charges of the fermionic particle; QCD
mass term coming from the Higgs mechanism instead of an explicit number
Weyl fermions; higher-dimensional generalizations; general understanding of spinors and other representations of Lie groups in maths
supersymmetric extensions
similar equations with a higher spin, e.g. the spin-3/2 equation for gravitinos
superstring theory as the final extension of the Dirac equation

If you think rationally about the beauty of the Dirac equation, and you're not constrained by taboos - e.g. a ban on the question where the beauty comes from you will figure out that the beauty really boils down to the properties of spinor representations of the Lorentz group. Once you know that, you want to know all kinds of similar "beauties". In other words, you should comprehensively learn and analyze the theory of representations of Lie groups and Lie algebras.