It is all over the garden, this short plant with little blue flowers. I a kind of like it, but what is it? The yard will be mowed soon, is it wise to move at least some of them to the corner for wide flowers, and let it grow?
It's a speedwell, most likely slender speedwell or Veronica filiformis; it is a common lawn weed in Europe, along with one or two other similar ones, V. chaemedrys, V. serpyllifolia and V. hederifolia. Slender speedwell is a highly invasive plant and is not usually planted in borders because it's difficult to control; this is also true of the others mentioned. Image in this link, along with other common lawn weeds, and recommendations for control http://www.lawnhealth.co.uk/lawn-weeds/identification/