A Lie Group is a Group + a Manifold - That's It

What is a Lie group?

The number line is R1. It is a 1-dimensional manifold; a 1-dimensional space. It is also a group, since all real numbers form an additive group. Therefore, the real number line R1 is a manifold and a group. A Lie group, after Norwegian mathematician Sophus Lie.

R2, R3, Rn are all Lie groups! :D