I am attending a course on elementary Lie algebra theory and I have trouble understanding something that we mentioned in class: If $\mathfrak{g}$ is a Lie-algebra and $\delta\in\text{Der}(\mathfrak{g})$ is a derivation, then $e^\delta$ is an automorphism of $\mathfrak{g}$ and this was left as an easy exercise.
There is something that I don't get here. How is $e^\delta$ defined? I guessed through $$\sum_{k=0}^\infty\frac{\delta^k}{k!}$$ but since we have not talked about any topology, I figured that this is not the case. What baffles me is that I cannot find any reference of this on any text I've been through. The most relevant thing I came across was exponential map of a Lie group, but we have not even talked about the notion of a Lie group.
Any help and any reference is greatly appreciated.