I take into account that lots of questions on Zoll surfaces have already been asked on the forum. But I will stubbornly continue asking. Are there any chances to *draw* explicitely at least one Zoll surface which is not of revolution? Is there some addition to the not at all explicit argument of V.Guillemin who proves that there are many Zoll metrics on the sphere (functional parameter family)? Guillemin uses inverse function theorem to prove this fact so no hope for explicit calculations...

This is so strange, people do work a lot in the domain of Zoll surfaces although I do not find almost any pictures for this on Internet.

Additional questions that perturb me:

Has somebody proven an existence of Zoll metric not close to the canonical one? (not by the "perturbation" argument?)

For the Zoll metrics in higher dimensions, even on the sphere $S^d$, do we have any examples except for the analogues of "revolution metrics"? That is, do we have any examples of metrics without symmetries?

What is known for Zoll metrics on the manifolds which are not $C^{\infty}$ smooth?

Is there a book on Zoll surfaces that is more digestible that A.Besse's

*Manifolds all of whose geodesics are closed*?

PS. I hope that this post could become a collection of the facts "known-by-now" on Zoll surfaces. I'm just getting lost in the abundance of information on the subject which is badly gathered. And I'm sorry that I do not have any picture in the post with the word "draw" in the subject.