Question: > 
> Let G be a group. For $g \in G$ write $l\_g : G \rightarrow G$ for the function $l\_g(g') = gg'$. Then $l\_g$ is a permutation of G. Moveover, if we define $\Lambda: G \rightarrow S(G)$ by $\Lambda(g) = l\_g$, then $\Lambda$ is an embedding. In consequence, if G is finite, then it is isomorphic to a subgroup of $S\_{|G|}$.
> 
> 
> 

My question:

What does "embedding" mean? Does it have a formal definition, or does it just mean a function that is not surjective? I tried to search the definition online but couldn't find anything useful.

Thanks in advance

Answer: 
Here it means an injective homomorphism.
In this case, *embedding* is being used to say that $G$ has a *copy* of itself into $S(G)$, that is, there exists an injective homomorphism onto its image.