As the chapter begins, you and Ellie will be on a horse. Enter the main university gate, then do a bit of exploring before heading up a ramp. When you get to the top of the ramp, look to your right and you'll see what looks like an open garage. Disembark from your horse, then go inside to find some loot and the first of the chapter's two crafting tables, as well as a Flamethrower.
Tip: You have a Bloater coming up, and although you can sneak past him, this is the perfect tool for the job. Try not to use this until we tell you to.
After upgrading at the crafting table, look for a door that is on the opposite wall and leads to some stairs. Head up the stairs and do some exploring, picking up any loot that you might find along the way. When you're done, head back to the horse and meet up with Ellie.
Continue riding a short distance further until you reach the top of some steps. Dismount from Callous, then search the building to the right, as well as the ground all around the area. When you're done, head into the building to the left. When you go through a gate, a cut scene will show that Ellie has caught up with you and the story will progress.
Beyond the gate will be what looks like a common building, and if you use Joel's focused hearing, you should see a lot of Infected on the upper level. This is also a good chance to use your Flamethrower, but we feel that it's a waste of perfectly good fire. Instead, think about using your Bow. The less bullets you use, the better.
Tip: You can also go with a Molotov in this situation. While you may not have as much luck as us, in a previous playthrough we managed to get every last one of them with a single toss.
When you're ready, head up the stairs toward the Infected, passing the door on your right and going all the way to the top. You'll be by a ledge near the back of the room, and from here you should be able to nail a couple of the Infected with the Bow. Be warned, at least one wanders out into the hall, so wait for it and then put an arrow through its skull. When all of the Infected are down, loot the area and start the generator.
Head back down to Ellie, open the gate and then hop back up on your horse. Go through the gate until you come to an opening. Make sure to dismount, then check the entire area for loot. When you're satisfied with your search, mount Callus one more time and go up another set of steps to the next area.
After jumping a short barricade, you'll come to a large area with a fountain and some monkeys running around. Head to the right building, jump through some windows and head up to the second floor. Jump onto the roof, then head left and you'll see another window you can go through. You'll find the Training Manual: Health Kit Sterilization on the desk.
Tip: There aren't any Infected in this area, so don't bother going stealth until we say so.
Make sure to cover the entire open area, going around and looking for anything and everything you can grab. When you're happy that you've picked it clean, get back on your horse and head in the only direction that leads you out of this area, then take a right. A very short distance along, Ellie will make a comment about Fireflies and you'll see a door partially blocked by debris. That's where you're headed.
Crawl under the debris and into the dorm area. Make sure to loot each room as you go, then head upstairs and do the same there. As you come to the last room, you'll encounter some spores and a hole in the floor. Before you jump down, make sure to do some crafting, as well as checking to see that your Flamethrower is equipped and ready to go.
As soon as you drop down, you'll be able to use Joel's focused hearing to spot four Clickers, and a Bloater that sits at the far end of the hall. If you have enough Shivs and they're upgraded, you can quite easily neutralize all four Clickers with stealth takedowns. In fact, that is likely your best option, since any type of loud action will cause the Bloater to come stomping your way.
When all four Clickers are dead, sneak up to where the Bloater is and throw a Molotov or two at him. In fact, two should do the trick, but one will cause him to thrash in pain, allowing you to just cook him with your Flamethrower. When the room is clear, make sure to loot it, then get the heck out of there.
Tip: Were you able to find the PlayStation Easter egg that sits on a low shelf near where you entered the area? If not, there's another on to be found in the next chapter.
Head upstairs, then take a right in the hallway and make sure to loot each of the dorm rooms. When you're done, backtrack to where you emerged and go the other way. Make your way back to Ellie and push the generator close to the gate, then fire it up to let her through.
Hop back on your horse, then continue along the way until you reach some tents. Make sure to check inside and around each one for supplies. You should find quite a few Parts, which is usually a sign that you are getting close to a crafting table, which you are.
When you come to a downward ramp that leads to a gate, disembark from your horse and look for the dumpster nearby. Push the dumpster to the top of the hill, then use it to smash through the gate. Once you're on the other side, grab the garbage bin one last time and push it against the truck, using it to climb up and gain access to the university's science building.
Now that you're inside the building, your main goal will be to find the Shiv door. When you enter, go into the hallway and turn right, it will be at the far end on the right. Open it up to find Tools Level 4 and the Training Manual: Molotovs Upgraded, giving them a larger blast radius. When you're done, go back into the hall and turn left, heading to the other end where you'll find a crafting table in a nearby room.
Tip: Do not use the crafting table until you use a Shiv to open the door. Tools Level 4 will allow you to make further upgrades, plus there are loads of Parts inside as well. In fact, search all the open rooms before using the table. You might as well have as many Parts as you can before you start choosing what to fix up and what to leave be.
As soon as you're ready, head out to the balcony and follow it around to a foyer with some stairs. Check the area, then go upstairs and take another balcony to the left and into a door with a three next to it. Start looting the area, going room by room as you continue down the hall and into a lab with a bunch of monkeys. Keep moving through a few more rooms until you trigger a cut scene.
When the scene is over, start backtracking to make your way out of the university. It's the same path you took to get where you are, just in reverse. Of course, things are complicated by the fact that a bunch of Hunters are after you, so stay low and utilize Joel's focused hearing.
Tip: If you're concerned about getting flanked, don't be hesitant to drop a Bomb at one of the choke points the enemy is bound to pass through.
As you get to the door of the room where you saw the monkeys, two attackers will burst through. Your best bet is just to wait for them and then go for the Shotgun headshot. With them down, exit the room and take a left at the hallway. After moving a few feet, you'll see some enemies enter the other end of the building. Back up, using the cover that's laying around, then think about using your Hunting Rifle to snag a few headshots.
Continue to move and shoot, using your focused hearing to get the drop on any Hunters. When you pass through the foyer and find a lone foe on the balcony, kill him and head for the door, triggering a scripted fight and a cut scene.
When you're back in control of Joel, start following Ellie, eliminating the Hunters as you go. When you finally do get back to your horse, you'll trigger a chapter ending cut scene, then it's on to Chapter 9: Lakeside Resort.