What kind of tree is the one in the picture?
From this photo and the additional photos you sent, the tree may a Fagus sylvatica Asplenifolia. Sometimes known as a Cut Leaf European Beech. It is challenging to identify a tree without close-ups of the leaves, and without being able to clearly see the arrangement of leaves on the branches. I suggest that you take a small branch with leaves on it to your local nursery – they may be able to identify it with certainty.
For a helpful tree identification resource, see the DePauw Nature Park field guide to trees.