Step 1: Recall classification of amines.
- A primary amine (1°) has one alkyl group attached to nitrogen (R–NH$_2$).
- A secondary amine (2°) has two alkyl groups attached to nitrogen (R$_2$–NH).
- A tertiary amine (3°) has three alkyl groups attached to nitrogen (R$_3$–N).
Step 2: Apply to given case.
In (CH$_3$)$_3$N, nitrogen is bonded to three methyl (–CH$_3$) groups and has no hydrogen directly attached to it.
Step 3: Identify type.
Since three alkyl groups are attached to nitrogen, it is a tertiary amine.
Step 4: Final Answer.
\[
\boxed{\text{Tertiary amine}}
\]