This paper presents a survey and some (hopefully) new facts on germs of maps tangent to the identity (in
R
,
C
,
\mathbb {R},\mathbb {C},
or
R
2
{\mathbb {R}^2}
), (maps
f
f
defined near
0
0
, such that
f
(
0
)
=
0
f(0) = 0
, and
f
′
(
0
)
f’(0)
is the identity). Proofs are mostly original. The paper is mostly oriented towards precise examples and the questions of descriptions of members in the conjugacy class, flows,
k
k
th root. It happened that entire functions provide clear and easy examples. However they should be considered just as a tool, not as the main topic. For example in Proposition
2
2
the function
z
↦
z
+
z
2
z \mapsto z + {z^2}
should be better thought of as the map
(
x
,
y
)
→
(
x
+
x
2
−
y
2
,
y
+
2
x
y
)
(x,y) \to (x + {x^2} - {y^2},y + 2xy)
.