firsthome - I believe what you have there is Ranunculus ficaria aka lesser celandine or fig buttercup. It's rather weedy and has some unique reproductive abilities that allow it to outcompete other things quite well. A documented problem is several areas of the country.

Here is a link that might be useful: lesser celandine

Thanks! That is it!

The picture on the website you provided shows a thick carpet of the fig buttercup....that is what the woods neighboring our yard looks like.

Now the trick is going to be trying to stop if from growing right into our yard. Any tips? Do you think if we put some sort of low retaining wall into the ground that would help? About how deep do the roots grow?

The roots are actually fairly shallow. The problem is that it has little reproductive structures called bulbils which are attached at the stem nodes. As the plant stems creep along the ground, they root at the bulbils, or worse, the bulbils break off in the soil and grow new plants or get moved through digging activities. The base of the plant also has finger-like tubers that can break off as well. Digging works for small groupings of plants, but you have to check back every year and make sure any germinating bulbils are removed. Too bad the woodland next door is so infested - I know it's a cute little thing but it sure can drive out the native plants. The good news? In about a month or so it will die back completely and vanish from view...until next February.