Today, when I was studying a mechanics textbook, I found something interesting. It was mentioned that symmetries and conservation laws are closely related. As an example, energy conservation corresponds to the time-translation symmetry in time (which means the laws of physics do not change according to time). The conservation of momentum corresponds to the space-translation symmetry, while the conservation of angular momentum has the rotational symmetry as its corresponding symmetry.
For detailed explanation of Noether’s Theorem, you might want to look at this post: http://gravityandlevity.wordpress.com/2011/01/20/problems-you-can-solve-just-by-looking-at-them-the-meaning-of-noethers-theorem/
Emmy Noether was a female German mathematician Emmy Noether, and her life story is quite interesting. Here is a New York Times article about Emmy Noether: http://www.nytimes.com/2012/03/27/science/emmy-noether-the-most-significant-mathematician-youve-never-heard-of.html