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I never noticed this plant in my garden. Now I see it in several places. Is this an aggressive invader? Or a well-behaved wild flower?

I don't mind its looks (even I like it in a way, its natural style; flowers are a kind of pleasing to the eye too), or location, just don't want to have zillions of them next year.

Zone 7a, continental Europe. Pictures taken today.

Looks like buttercup (Ranunculus). Very common in the Netherlands, I think it is not harmful (but it is poisonous). The story about the name is that the flowers were used to give the yellow color to butter, but it is probably not true this story.

The story about buttercups giving butter its yellow colour is certainly false, because it is poisonous to cows and other farm animals, and also to humans.

Presumably it is also poisonous to domestic pets. However its toxicity is not usually a serious problem, because its taste is so bad that nothing will eat it unless there is no alternative food available!

It spreads mainly by sending out runners which root and form new plants. Your garden won't be overrun by buttercup seeds germinating everywhere, but it will spread quite fast, and you don't want it in your lawn for example. It dies down in early summer and the tuberous roots are dormant in the soil till the following spring, so once it has finished flowering it "disappears" and is hard to eradiate.

The "wild" species in your pictures really belongs in a hay meadow, not a garden. There are some cultivated varieties sold as flowering plants, see https://www.rhs.org.uk/plants/search-results?form-mode=true&context=l%3Den%26q%3DRanunculus%26sl%3DplantForm&query=Ranunculus for example.