Episode 2 of the Amazon Prime series sees our characters entering the ruins of a long-abandoned city to escape the pursuing trolloc hordes. Moiraine gives a brief history of what befell the city and how it came to be abandoned.
Our characters then enter the city and events ensue that end with them being split up and left to fend for themselves without the protection of the Aes Sedai. Unfortunately, a lot of events were cut out or altered in the TV series and this has led to characters making decisions without context as to why those decisions were made(Mat picking up the dagger).
So, without further ado, here are how the events of Shadar Logoth played out.
Of course, it still starts with Mat
After they enter the city and Lan begins taking care of Moiraine. Mat expresses a desire to go out and explore. Rand wants them to ask Moiraine but Mat convinces him she would never let them go. The three eventually sneak out of the building to explore.
The three set off on their adventure and as backwater, farmboys are enthralled by the city; abandoned and decrepit as it was.
Mat wanted to see everything, it seemed, and he pulled the others along with his enthusiasm. They climbed over dusty fountains with basins wide enough to hold everybody in Emond's field and wandered in and out of structures chosen at random, but always the biggest they could find.
- Excerpt from "The Eye of the World" by Robert Jordan
They explored for some time looking for treasure but after finding nothing but dust decided to give up. Then, a man suddenly came up to them.
He introduced himself as Mordeth and told them he was a treasure hunter. He then explained that he had found and collected a large treasure hoard but he needed help getting it out of the city and he promised to give them a share if they could help him take the treasure.
Rand and Perrin were skeptical but Mat's eyes lit up at Mordeth's words. He overruled their objections and the three soon found themselves following Mordeth deeper into the columns.
Mordeth, true to his words; led them to the treasure trove and the three farmboys were taken aback by the amount of wealth in the room.
Then the corridor ended in a tile-walled room and he forgot about any oddities Mordeth might have. His gasp was an echo of his friends'. Here, too light came from a few torches staining the ceiling with their smoke and giving everyone more than one shadow but that light was reflected a thousand times by the gems and gold piled on the floor, mounds of coins and jewelry, goblets and plates, and platters, gilded, gem-encrusted swords and daggers, all heaped together carelessly in waist-high mounds.
- Excerpt from "The Eye of the World" by Robert Jordan
Rand managed to keep himself levelheaded and soon noticed that Mordeth didn't cast a shadow. He cried out a warning to his friends and Mordeth suddenly began to expand and growl. The three scrambled for safety and ran out of the rooms. They didn't stop running until they finally got back to Moiraine and the rest.
Moiraine questioned them on what happened and on getting the details, asked them if Mordeth had given them anything. They all answered that he hadn't and even though Mat had taken a dagger, he convinced himself that he took the dagger, Mordeth didn't hand it to him.
Not long after, Lan came back from patrol with news of the Trollocs within the walls. This forced them to try and flee Shadar Logoth immediately.
At this point, the TV series reconciled events with the books, and they were all split up trying to make their way out of the city.