Blue flowers on the right in the top photo and in the second are Vinca minor...they belong to the shiny oval leaves. The blue daisy-like flower looks like Anemone blanda...and it is being overrun by the vinca.

The thinner, bright green rosettes of foliage are a Galium but can't see enough of it to determine which one. If they are kind of sticky to the touch, then Galium aparine or bedstraws - a weed. If not, they could be Galium odoratum, sweet woodruff, a shade loving groundcover.

Leaf shape etc. is that of Galium aparine. Whereas G. odoratum looks like this:

https://www.bing.com/images/search?q=galium+odoratum&qpvt=galium+odoratum&FORM=IARRSM

As winberry said. The Gallium is fairly certainly G aparine, not woodruff. And for good measure you have Glechoma hederaceae, Alliaria petiolata and Ranunculus repens in the mix. In my book the only one you need to care about in a garden setting is the Anemone blanda. The rest are weeds, except the Vinca which is a useful but very rumbustious creeping vine which can look after itself.

Wooded sites in my area have huge patches of Vinca minor dominating the forest floor. Eastern North American information sources addressing such things are calling it a problem plant.

OK, so the Vinca counts as a weed too, if the OP is in a vulnerable area.

Oddly enough, I live surrounded by a lot of natural wooded area plus my business travels take me to a lot more but I have never seen any feral patches of vinca in my portion of the PNW!! Plenty of ivy and yellow archangel, a few random splotches of ajuga or sweet woodruff but no escapee vinca!

Vinca is a fairly common escapee in the woods here in New England.

The plant at the top of the first photo with scalloped edges, Alliaria petiolata, is a real problem plant. Don’t let it flower and set seed which it will be doing very quickly. Pull it and put it in a bag in the trash.