Some kind of crab apple? I wonder why you would want to cut back such a young tree? If it is already too big it has been planted in the wrong place as it will get much larger than this and regular cutting back will spoil the shape.

Thanks for your help. The tree has plenty room to grow. I just did not want to let it grow too high if I was supposed to trim and keep it under control.As it is such a beautiful tree, I just want to do the right thing. As the branches are leaning to one side, should I perhaps tie them round a stake in the ground? As a beginner to gardening, all help is very welcome. Thank you again.
Alena

Looks like a malus to me (crab apple) - it's very pretty. I've got a one with very dark foliage and very dark red blossom. I lightly trim the height and any stray branches sticking out, after it has flowered, at the end of the summer, taking about 4" off it

Definitely a flowering crabapple (Malus species or hybrid). I saw a lot of them in Flagstaff, AZ, in my college days, but a real expert would be needed to identify the variety. They bloom on wood 2-10 years old, so pruning should be light, and directed toward structural issues--i.e., crossed branches, narrow crotches.

I wouldn't consider pruning the malus unless, as Tugb. says, there are structural problems. That is going to grow into one very big tree.

Looks like a crab apple to me.

Thank you to all with help on my questions. I will probably need your help further guiding me through the growing of my beautiful tree. Wish me luck!
Alena

That's what we are here for Alena... we love questions!