Species question

Hi, does anyone know this tree species?

PS: The bark on the photo is wet, so it's darker as usual.

Ulmus campestris

Pascal is right. It's an Elm. I have trouble keeping up with name changes though What used to be known as Ulmus Campestre and Procera, is now known as Ulmus Minor.

Oh dear. Can you get hold of a good field guide? It's not an elm. The leaves of Ulmus minor, & most of the elm family, have a distinctive uneven leaf base, like Begonia. These leaves look like hornbeam, but the bark doesn't match European hornbeam, nor weeping birch either. You'll have to catch it in bloom to get a better ID. Meanwhile, fire up your Google.
Iris

I thought it was the hackberrys that had the uneven leaf base.

They do. Hackberry, Celtis sp., belong to the elm family. If you look at elms, hackberries, and zelkovas, they all have that distinctive trait.
The only exception I know of is water-elm, Planera aquatica, an American member of the elm family that is occasionally used for bonsai. Its leaf bases are pretty even, sometimes just a tiny bit off.
Iris

This is definitely Elm. European of some sort. The bark has Elm written all over it. Your right about the leaves being offset but it can be by a very small margin sometimes.

Dorothy, I agree with Will : sometimes the uneven base of the leaf is not so evident.

To me it is definitely an umlacea. If it is not endemic to the region where the leaves were photographed, it may be a species of zelkova, like zelkova nire (rough bark zelkova) for instance, although the leaves of zelkova are usually larger. So it should be an elm...