This weed with very small white flowers and is invading my yard. What is it and how do I control it without killing my grass.
How many petals do the flowers have?
It looks as though it could be in Rubiaceae, similar to Diodia, a pesky weed in lawns.
Here is a link that might be useful:
Diodia virginiana, Virginia buttonweed, is a wild flower that is fairly common in wetlands but has been spreading out and becoming a noxious "weed".
Control can be difficult since these plants prolifically produce seeds and can root from stems as well as the rhizomes which grow very deep into the soil. Mobile Botanical Gardens people tell us this is a very difficult plant to eradicate and few herbicides are effective at control. Persistent hand removal is probably the most effective method.
Here is a link that might be useful: Diodia virginiana
Looks more like Hedyotis corymbosa, to me....at least from that particular image.
Here is a link that might be useful: Hedyotis