Symmetry carries the connotation of beauty. Mathematized, it is a deep and reoccurring theme in the Book of Nature. Many unexpected properties of reality are uncovered by it. A key concept related to symmetry is invariance, the simple property of a system to remaining unchanged under manipulations. Invariance has the power to unlock fundamental knowledge. Level of mathematical formality: high (however, the mathematically involved parts are encapsulated and demarcated by the tags { ' . . . ' },

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... ence easily bypassed). The notion of symmetry carries with it the connotation of beauty, harmony and unity. In the words of Hermann Weyl (1952, p. 5): Symmetry, as wide or narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection.