Let $(\mathbb{E}, \pi, \mathbb{B}, \mathbb{F})$ be a Fibre Bundle and $\mathcal{F}$ be a $C^r$ (where $r \ge 1$) Foliation on $\mathbb{E}$ that is Transverse to the fibres of the fibre bundle $(\mathbb{E}, \pi, \mathbb{B}, \mathbb{F})$.
Let $\pi_1(\mathbb{B},b)$ be the Fundamental Group of $B$ at a base-point $b\in B$ and $Diff^r(\mathbb{F})$ be the group of $C^r$ diffeomorphisms of $\mathbb{F}$.
Then, there is a Representation $$\varphi:\pi_1(\mathbb{B},b) \longrightarrow Diff^r(\mathbb{F})$$ called the Holonomy of the foliation $\mathcal{F}$, by the way $\varphi$ is just a Group Homomorphism.
The question is
How to construct this representation $\varphi$?