I'm sure that is Bermuda grass, it will stay brown until the weather warms up a bit more and WILL outcompete your lawn grass during the late spring and summer.
You should defiantly take a clump of it to a nursery or extension office to verify that it is Bermuda Grass.
You should do some google searches to find what will work best for your area, but I'm guessing a lot of roundup... Digging... More roundup... Digging... Then maybe you can reseed/sod those areas. Good luck!