Lie groups have been a major focus of mathematical research for the last century, in a large part due to the connections between their three mathematical 'structures.' In this talk, we will follow John Milnor's classic paper, 'Curvatures of Left Invariant Metrics on Lie Groups,' and examine in some detail the deep interplay between the geometric propeties of Lie groups and the algebraic structure of the associated Lie algebra. The main result will be a classification of 3-dimensional Lie algebras.

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