Let $M$ be a manifold.
In the Example1.3. of Topological Methods in Hydrodynamics (V.I.Arnold, B.A. Khesin), it is written that diffeomorphisms preserving the volume element in a domain $M$ form a Lie group.
How is this topology defined? It is not explained before Example1.3..
Added
Now I understand how to define the Whitney topology for this group $\text{SDiff}(M)$. However, are $\text{SDiff}(M)$ and $\text{Diff}$(M) differentiable manifold?
You take the Whitney $C^\infty$-topology. A basis of this is given by $$S^k(U) = \{ f \in C^{\infty}(M,M) : (J^kf)(M) \subseteq U \}$$ where $k$ runs over all integers and $U$ over all open subsets of $$J^k(M,M).$$The latter is the space of $k$-jets of smooth maps $f \in C^{\infty}(M,M)$, its topology is defined in https://en.wikipedia.org/wiki/Jet_(mathematics)#Jets_of_functions_from_a_manifold_to_a_manifold