Errata for the book:
The convenient setting of Global Analysis
Misprints and additions in the book:
The convenient setting of Global Analysis,
by Andreas Kriegl and Peter W. Michor
June, 2000. August, 2008. March, 2015.
Please, send any other misprints to
<Peter.Michor@univie.ac.at>
page_{line number from below}
page^{line number from above}

x_1: remove the DOSgremlin

1_{16}: on a finite dimensional compact smooth manifold

27: In second display from bottom: \sum_{i=0}

56_12 Omit the last sentence.

66 In 5.26 Theorem: ... Then $C^\infty(U,F)$ is convenient and satisfies ...

106^4 Wording of Definition

116^4: Italian

116_5: The Portuguese

127: In 12.7 Lemma: replace `locally bounded' by `bounded on compact sets'.
Some changes in the proof required. (Noted by Helge Glöckner)

187_8 not measurable

332^7: one `each' is too much

369^{11}: is to assume that

374^1: Proof of (2).

374_5: Proof of (3).

429^{14}: on a finite dimensional compact manifold

450:
The proof of Theorem 42.21 works only for a finite dimensional structure
group. (Noted by Christoph Wockel)

451^{16}: u=(\exp_V)^{1}:U\to V

453_8: TM as last entry in the display

456 In 43.2 Example ... that
$\Diff(M)$ contains a smooth curve through $\Id_M$
whose points (sauf $\Id_M$) are free generators of an arcwise connected free
subgroup which meets the image of $\Exp$ only at the identity.

474_{15}: submani\fold

475: More details in the proof of theorem 44.1 added.

475_2: C^\infty_c

476^{20}: $N$ twice,

476: The statement of 44.2 is enlarged and proofs have been included (10 pages more).

498^6: De Vrie{\ss} > De Vries (often!)

499_2:
+\frac{k_x(h\ell)_x}{f_x^2}

499_1
+2f_xhk_x\ell_x 2f_xh_xk\ell_x\Bigr)

501_1:
= \ad([X,Y]_\g)^\top.

503_1:
+\tfrac14[\al(y),\al(u)]u

508_2:
$$\align
b_{tt}
&= \int_{S^1}(y_{txxx}u + y_{xxx}(3u_xu+au_{xxx}))dx \tag{\nmb{2}'}
\endalign$$

523^6 Then $\ell'$ is a Lie algebra homomorphism.

523 In 48.2 replace the second paragraph by the following which is needed in the proof of 48.8
Theorem (Otherwise it is wrong):
A $2$form $\si\in\Om^2(M)$ is called a
{\it weak symplectic structure}\index{weak symplectic structure}
on $M$ if the following three conditions holds:
\begin{enumerate}
\item[(\nmb:{1})] $\si$ is closed, $d\si=0$.
\item[(\nmb:{2})] The associated vector bundle homomorphism
$ \check\si: TM \to T^*M$ is injective.
\item[(\nmb:{3})] The gradient of $\si$ with respect to itself exists and is smooth;
this can be expressed most easily in charts,
so let $M$ be open in a convenient vector space $E$. Then for $x\in M$ and
$X,Y,Z\in T_xM=E$ we have
$d\si(x)(X)(Y,Z)= \si(\Om_x(Y,Z),X) = \si(\tilde\Om_x(X,Y),Z)$
for smooth $\Om,\tilde\Om: M\x E\x E \to E$ which are bilinear in $E\x E$.
\end{enumerate}

525 In 48.8 Theorem insert:
We equip $C^\infty_\si(M,\mathbb R)$ with the initial structure
with respect to the the two following mappings:
$$
C^\infty_\si(M,\mathbb R) \East{\subset}{} C^\infty(M,\mathbb R),\qquad
C^\infty_\si(M,\mathbb R) \East{\on{grad}^\si}{} \X(M).
$$
Then the Poisson bracket is bounded bilinear on $C^\infty_\si(M,\mathbb R)$.
before:
We have the following long exact sequence of Lie algebras

526 Many changes in the proof of the theorem.

527_{16}: remove `er' and a second = sign

549^{16}: Omit sentence "All these norms ..."

609^{10}: Grundz\"uge