It looks like a birch tree of some variety so it could grow to 20 or 30 feet high.

I would also say a Birch. The problem with them is that they hate pruning to keep them smaller that their eventual height. You certainly never prune them between spring and summer as they bleed sap and attract lots of insects and diseases which will attack it. The good news is that they are light and give dappled shade, so it is not a light blocker in a garden.

We have several Betula (birch) trees of different species in our garden and I love them. They are very stately and give dappled shade as Kildermorie says. Just what is needed when the temperatures go into the upper 20s.

Just don't plant it near to the house, the roots will even move paving slabs, beautiful trees though