Does Anyone Know what Plant this is??

My Dad transplanted this to his yard a few years ago but can't remember it's name.

I plan on digging some of his up so that I can plant a bit in my yard.

It comes back each year on it's own and I think it is so pretty and delicate looking. It almost looks like a flower inside of a flower.
Just wish I knew what it was!

I've still got plenty of photos to share with you all from our trip but I've been super duper busy trying to wrap up our schooling for the year and attempting to get my Spring Cleaning begun.
Hope to be back tomorrow with a few more of those photos PLUS I'm way behind on reading all of your blogs. I'll be around to visit all of you soon!