For any class
M
\mathcal {M}
of 4–manifolds, for instance the class
M
(
G
)
\mathcal {M}(G)
of closed oriented manifolds with
π
1
(
M
)
≅
G
\pi _1(M) \cong G
for a fixed group
G
G
, the geography of
M
\mathcal {M}
is the set of integer pairs
{
(
σ
(
M
)
,
χ
(
M
)
)
|
M
∈
M
}
\{(\sigma (M), \chi (M)) | M \in \mathcal {M}\}
, where
σ
\sigma
and
χ
\chi
denote the signature and Euler characteristic. This paper explores general properties of the geography of
M
(
G
)
\mathcal {M}(G)
and undertakes an extended study of
M
(
Z
n
)
\mathcal {M}(\mathbf {Z}^n)
.