  We develop silting theory of a noetherian algebra $\Lambda$ over a
commutative noetherian ring $R$. We study mutation theory of $2$-term silting
complexes of $\Lambda$, and as a consequence, we see that mutation exists. As
in the case of finite dimensional algebras, functorially finite torsion classes
of $\Lambda$ bijectively correspond to silting $\Lambda$-modules, if $R$ is
complete local. We show a reduction theorem of $2$-term silting complexes of
$\Lambda$, and by using this theorem, we study torsion classes of the module
category of $\Lambda$. When $R$ has Krull dimension one, we describe the set of
torsion classes of $\Lambda$ explicitly by using the set of torsion classes of
finite dimensional algebras.
