Well, it's a Giant but almost certainly not the one we're familiar with. Giant started out in 1972, contract manfacturing bicycles. Their own brand didn't appear until 1981 and this one looks older than that. It looks like the crankset may be an upgrade. The rear derailleur resembles a Campagnolo Nuovo Gran Sport, though it could be a Zeus or Triplex copy. It's likely a boom era, private label brand. I'm wondering if it's origin is Italian? Some more detail pics would be great. I'm very curious.