Is there a non-matrix Lie group?

Question

I'm new to Lie Groups, but all the examples I found are matrix groups. Can someone show a non-matrix Lie group?

Answer 1

There is the metaplactic group, which is the unique connected double cover of the symplectic group.

Answer 2

Lie groups are smooth manifolds. They may or may not have matrix representations. For example, the universal cover of $\mathbf{SL}_2(\mathbf{R})$ is a Lie group that is not a matrix Lie group.