There's plenty to take notes on and plenty of need to take notes on it because it isn't designed to be memorable. There's conveniently an episode about different kinds of magic known here.
"...I'm Mahan and I will be teaching you Hari," says the show's host. "Today we'll talk about magic. This is Ariu. Ariu is an illusion mage. Ariu will show us illusion magic now." There's a good view of a bare patch of ground between them. And then projected on that patch of ground are twelve symbols. "This is an illusion of magic. We call it that because there are twelve kinds." ("Magic" and "twelve" are the same word in Hari.) "You are watching Hari is the Language of the Empire on an enchanted object. It is enchanted with illusion magic. This is the symbol for illusion magic." He points to it with his tail. "I am a void mage. Using void magic is against the law. Do not use void magic. This is the symbol for void magic."
A snake slithers into view. "This is Agi. Agi is a force mage. This is the symbol for force magic. Agi will do some force magic." Agi levitates. "Agi is levitating by using force magic."
Agi slithers off, to be replaced by another furry creature who does sun magic. The furry creature transmutes elements. The symbol for sun magic looks like a sun.
Other kinds of magic are explained, but not clearly enough for someone with no experience with local magic and no knowledge of Hari to understand.
The next episode probably goes mostly over her head. It includes the word for blood! And war! It's some kind of history lesson.
They cover common materials. (This is coal, coal is the sixth element, this is wood, wood's not an element, this is a candle, the candle is on fire, the fire is using vital air, vital air is the eighth element. This is steel, steel can't be made by a sun mage but can be made by a structure mage. This is silver, silver is the forty-seventh element, it can be made by sun mages...) They cover common activities like eating, sleeping, going to work, going to buy things. They demonstrate questions and answers. They name foods. (Apple, peach, pecan, mutton, snapper...) They demonstrate the local currency, which is what Valanda's necklaces are for.
In one episode Mahan has a large box and narrates where he is in relation to it. "I am getting into the box. I am in the box. I am sitting in the box. I am getting out of the box. I am beside the box. I am outside the box. I am in front of the box. I am still outside the box. I am beside the box again. I am on the opposite side of the box now. I am turning the box upside-down. I am on top on the box..."