What makes Lie Groups a crucial theory in modern dynamics and beyond?

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http://arxiv.org/abs/1104.1106
Lecture Notes in Lie Groups
Vladimir G. Ivancevic, Tijana T. Ivancevic
(Submitted on 6 Apr 2011)
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engineering and biomechanics. The only necessary background for comprehensive reading of these notes are calculus and linear algebra.
Comments: 58 pages, 4 figures
 
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These guys are pretty good. They've also got some nice notes on TQFT and De Rham–Hodge Theory that are well worth checking out.