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Classical mechanics can be understood very well in the context of ordinary differential equations. In the physical world, we observe some phenomena which are not explained by classical mechanics (quantum tunneling, double-slit diffraction). Hence, classical mechanics is an incomplete description of physics, and better theory is required. This talk will start with an overview of the process called "quantization of a classical system", with particular focus on harmonic oscillators. We will find the representation theory of Lie algebras (and Lie groups) to be intrinsically useful in this context. Time-permitting, we will discuss a physical interpretation for decompositions of tensor-product-representations into irreducible representations.