The author exhibits sharp embedding constants for Sobolev spaces of any order into Zygmund spaces, obtained as the product of sharp embedding constants for second-order Sobolev spaces into Lorentz spaces. One of the excellent results reads as follows. Let \(n> 2\), \(q> 1\), and \(\Omega\) be a bounded domain in \(\mathbb{R}^n\). Then, the following embedding holds: \[ \begin{gathered} W^2 L^{n/2,q}(\Omega)\cap W^1_0 L^{n/2,q}(\Omega)\to Z^{q-1/q}(\Omega),\text{ namely,}\\ \| u\|_{Z^{q-1/q}}\leq \gamma_{n,2}\|\Delta u\|_{n/2, q}\end{gathered}\tag{1} \] for any \(u\in W^2 L^{n/2,q}(\Omega)\cap W^1_0 L^{n/2,q}(\Omega)\), where \(\gamma_{n,2}= \omega^{{-2\over n}}_n[n(n-2)]^{-1}\) and \(\omega_n= \pi^{{n\over 2}}/\Gamma({n\over 2}+ 1)\) is the volume of the unit ball in \(\mathbb{R}^n\). Moreover, the constant appearing in equation (1) is sharp. As an easy consequence of this result, the author then gives a new proof of Adams’ inequality, which holds under the weaker hypothesis of homogeneous Navier boundary conditions.