References for endomorphism bundle and adjoint bundle I am trying to understand what are endomorphism bundle(of a vector bundle) and adjoint bundle(of a principal bundle) but could not find any references on google.
Searching  Adjoint bundle gives https://en.m.wikipedia.org/wiki/Adjoint_bundle which does not really say much. But searching endomorphism bundle does not give anything.
Any reference is welcome.
Endomorphism bundle came in context when discussing about curvatures. It has been said that Curvature can be seen as section of some endomorphism bundle.
 A: Here is a short answer regarding the endomorphism bundle of a vector bundle $E\to M$. The fiber of $\mathrm{End}(E)$ at a point $p\in M$ consists of all linear maps $E_p\to E_p$. This fiber is clearly a vector space. Furthermore, if $E$ is trivial in the open set $U\subset M$, then so is $\mathrm{End}(E)$. Hence, $\mathrm{End}(E)$ is indeed a vector bundle, and a section of this bundle is to be understood as a smooth family of linear maps $E_p\to E_p$ for $p\in M$.
If you like operations on vector bundles, you may like the natural identification$$\mathrm{End}(E)=E\otimes E^*.$$
Edit: Let us see how the endomorphism bundle arises naturally when playing with curvature. Let $E\to M$ be a vector bundle equipped with a linear connection $\nabla$. Let $X$ and $Y$ be vector fields on $M,$ and let $s$ be a section of $E$. We define $$R(X,Y)(s):=\nabla_X\nabla_Ys-\nabla_Y\nabla_Xs-\nabla_{[X,Y]}s.$$ Then one can show that $R$ is in fact tensorial in all its arguments. Moreover, as $R$ is clearly anti-symmetric in $X$ and $Y$, it is a $2$-form on $M$ with values in the vector bundle $\mathrm{End}(E)$. This $R$ is called the curvature (or curvature form) of $\nabla$.
