Stray Notebooks can be found hidden away in various locations within The Slums, and if you want to progress the storyline then you'll need to gather them up to recover the Outsiders' research notes compiled by Momo, Zbaltazar, Doc and Clementine. The information they've recorded between them is essential for establishing communication with those outside of the area, but you'll need all of the component parts before you can put together a plan for reaching out to others. Although this task is presented as a side quest, you won't be able to move on from The Slums until you complete it, so here's how to find all four Stray Notebooks locations so you can proceed to unlock the Rooftops.
Note that although the Stray Notebooks are numbered from 1 to 4, they can be collected in any order and you don't need to meet Momo first before collecting the other three documents, so as with finding the code for the safe in Stray you can approach this assignment in any order you like. Finding the books is all that's important here so you can move on.
How to fix the Stray Notebook glitch
Some players are reporting a Stray Notebook glitch, where either the collected Notebooks are not appearing in their inventory or Momo won't accept them, which prevents them from completing this quest to continue with the story. If you encounter this Stray Notebook bug, then pause the game and reload last checkpoint which should resolve the issue. If that still doesn't work, then you'll need to quit to the main menu then restart The Slums chapter, though thankfully it shouldn't take you long to repeat your progress and get back to where you were before.
Stray Notebooks 1/4 - Momo
As soon as you arrive in The Slums, the first task you'll receive from the Guardian is to go and see Momo, who is in the high up building with the orange neon sign. There are plenty of different routes to get up there and the sign is an obvious landmark to aim for, though if you're struggling then get on to the roof of the bar then look towards the sign while heading forwards and upwards. When you get there, a couple of hops on AC units will get you to the balcony, where you can climb in through the window. If you haven't done a Stray Scratch for this chapter yet, then get your claws stuck into Momo's rug.
Once inside, meet Momo and show him the postcard, at which point he'll tell you his woes with building the Transceiver and falling out with his friends. He'll also give you Momo's Notebook as part of this dialogue, which is one of the four Stray Notebooks you need to complete the set. You can also pop through the beaded curtain into the bedroom area while you're here, to collect one of the Stray B-12 Memories by scanning the video game poster on the wall.
Stray Notebooks 2/4 - Zbaltazar
Make your way to the rooftop with the higher of the two paint pot throwing robots, then go past the pulley and follow the string of lights up to a higher level with a fan spinning between some AC units. On the side you'll find a sign reading "Ventilation power supply" along with a breaker you can interact with to remove it. This turns off the spinning fan, allowing you to jump down to the room below.
When you're in there, hop down from the bunk bed and look for a stack of boxes in the middle of the room, which you can knock over by leaping on top of them then jumping off again. Check the now open box that fell off, and inside you should find Zbaltazar's Notebook, the second of the Stray Notebooks in the set.
Stray Notebooks 3/4 - Doc
In one of the top corners of the rooftops, you'll find a TV and sofa underneath a string of lights – if you sit there and flick through all of the channels you'll earn a trophy in the process. There's also one of the Stray energy drink locations just below this platform, if you haven't found it already. Follow those lights to the balcony behind the sofa with lanterns and a blue sign, where you'll find a gap in the door to access the library.
In the rear corner of the library, you'll find a little den tucked behind some piles of books. Climb inside, then translate the note left on the bed, which will supply you with the safe keys as well as a clue for where to find it.
Back in the main library room, look for the safe which is not particularly well hidden behind several stacks of books, then knock them over so you can access the door. Interact with the safe and use the keys to open it, then pick up Doc's Notebook from inside to receive the penultimate entry in the Stray Notebooks. If you check the piano around the corner in the library, you can also find one of the Stray Sheet Music locations while here, to work towards one of the Stray Badges.
Stray Notebooks 4/4 - Clementine
Climb onto the rooftop of the bar, then look for a window above you on a blue wall with yellow light shining from inside. Hop up along the pipes running around the building, and you'll soon be able to jump through the window.
Inside the apartment, head through a gap in the door to the bedroom area, then on your left you'll find a small side room with lots of books. At the end of that room is a computer, and if you hop up onto the desk you can grab Clementine's Notebook from the top of a monitor.
This completes your collection of Stray Notebooks, and once you give them all to Momo you can move on to the next chapter in the story.
