  We discuss embedding of manifolds in the category of open books, contact
manifolds and contact open books. We prove an open book version of the
Haefliger--Hirsch embedding theorem by showing that every $k$-connected closed
$n$-manifold ($n\geq 7$, $k < \frac{n-4}{2}$) admits an open book embedding in
the trivial open book of $\mathbb{S}^{2n-k}$. We then prove that every closed
manifold $M^{2n+1}$ that bounds an achiral Lefschetz fibration, admits open
book embedding in the trivial open book of
$\mathbb{S}^{2\lfloor\frac{3n}{2}\rfloor + 3}$. We also prove that every closed
manifold $M^{2n+1}$ bounding an achiral Lefschetz fibration admits a contact
structure that isocontact embeds in the standard contact structure on
$\mathbb{R}^{2n+3}.$ Finally, we give various examples of contact open book
embeddings of contact $(2n+1)$-manifolds in the trivial supporting open book of
the standard contact structure on $\mathbb{S}^{4n+1}.$
