This document derives useful formulae for working with the Lie groups that represent transformations in 2D and 3D space. A Lie group is a topological group that is also a smooth manifold, with some other nice properties. Associated with every Lie group is a Lie algebra, which is a vector space discussed below. Importantly, a Lie group and its Lie algebra are intimately related, allowing calculations in one to be mapped usefully into the other. 李群学习资料，侵删。