Need help replacing light fixture
Hook it up exactly like the old lamp was

Do not disturb any of the uninvolved wires: this is the mistake that gets a lot of people into trouble, they take them all apart and then get confused. Every wire has a job.  They are not color coded; the color codes are to distinguish the wires in a cable and are not reliable for indicating a meaning or purpose.

The old fixture had 2 blacks and 2 whites simply because it had 2 bulbs.  It's no big deal.  Put the new lamp's white wire where the old lamp's white wires went.   Ditto black.   That is all.  

The blue wire is obviously not ground, since it has a black wire going to it.  One of the few reliable color codes is that green, yellow-green stripe, and bare wires are always and only ground.  I doubt that is a ground wire, I believe it's a blue wire and your house is wired in metal conduit.  Conduit allows arbitrary wire colors to be used (which can make colors more meaningful) and metal conduit provides a ground path so fewer ground wires are needed.