Looks like an axle shaft boot. So here are the options I see based on my (limited) experiences over time.
1) Its just the boot. No damage to U-joints inside, get a split boot (use them a LOT on VW's), cut the old off, put the new on, forget about it. (This is easiest/cheapest scenario but a total Mickey Mouse fix...)
2) Pull your hub and replace the boot with a new OEM or equivalent, pack with grease, put on proper retaining clips, reassemble hub. Move one with your life. (Very good fix but only works if the axle, again, isn't damaged internally)
3) Buy a brand new or remanufactured axle shaft (new boots, U-joints, etc). Reassemble hub, move on with your life knowing its safe and functional for the long haul.
If you know all of this already, I don't mean to condescend. Just stating what decisions I would be faced with in the same scenario.
SIDEBAR... is that just dirt collected on the hydraulic line or is that actual damage to said line? I think its the brake line but not sure from the picture. IF its damage, you are going to want to replace that. If its just dirt, who care.... you're good!
Hope that helps?