The Burnside ring
B
(
G
)
\mathcal {B}(G)
of a finite group G consists of formal differences of finite G-sets.
B
\mathcal {B}
is a contravariant functor from finite groups to commutative rings. We study the natural endomorphisms of this functor, of its extension
Q
⊗
B
\textbf {Q} \otimes \mathcal {B}
to rational scalars, and of its restriction
B
↾
Ab
\mathcal {B} \upharpoonright {\text {Ab}}
to abelian groups. Such endomorphisms are canonically associated to certain operators that assign to each group one of its conjugacy classes of subgroups. Using these operators along with a carefully constructed system of linear congruences defining the image of
B
(
G
)
\mathcal {B}(G)
under its canonical embedding in a power of Z, we exhibit a multitude of natural endomorphisms of
B
\mathcal {B}
, we show that only two of them map G-sets to G-sets, and we completely describe all natural endomorphisms of
B
↾
Ab
\mathcal {B} \upharpoonright {\text {Ab}}
.