Quick question about functionality

I'm pretty new to this, and I've been going through the documentation, but I have a question about something I'm considering for my site...

Is it possible to allow users to place images or albums from the main gallery into their personal gallery, kind of like a favorite images" sort of deal. I don't want to allow them to upload images, but I'd like for them to have a gallery that they can collect albums or images in.

Just wondering if that's possible.

Thanks