  The second eigenvalue of the Robin Laplacian is shown to be maximal for the
disk among simply-connected planar domains of fixed area when the Robin
parameter is scaled by perimeter in the form $\alpha/L(\Omega)$, and $\alpha$
lies between $-2\pi$ and $2\pi$. Corollaries include Szeg\H{o}'s sharp upper
bound on the second eigenvalue of the Neumann Laplacian under area
normalization, and Weinstock's inequality for the first nonzero Steklov
eigenvalue for simply-connected domains of given perimeter.
  The first Robin eigenvalue is maximal, under the same conditions, for the
degenerate rectangle. When area normalization on the domain is changed to
conformal mapping normalization and the Robin parameter is positive, the
maximiser of the first eigenvalue changes back to the disk.
