Civilized Realms
The City-States of Tilea +4 - Extensive Imperial / Extensive Dwarven
The Empire of Man +7 - Extensive and Esoteric Imperial / Extensive Dwarven
The Kingdom of Bretonnia +6 - Extensive Imperial / Extensive Bretonnian / Extensive Dwarven
The Kingdoms of Estalia +4 - Extensive Imperial / Extensive Dwarven
The Kingdom of Kislev +4 - Extensive Imperial / Extensive Dwarven
The Karaz Ankor +9 - Extensive and Esoteric Imperial / Extensive Bretonnian / Extensive Dwarven
The Asrai of Athel Loren +4 - Extensive Imperial / Extensive Dwarven
The Eonir of Laurelorn +7 - Extensive and Esoteric Imperial / Extensive Dwarven
The Ten Kingdoms of Ulthuan +6 - Extensive Imperial / Extensive Bretonnian / Extensive Dwarven
I'd like Mathilde to have a more-or-less complete reference library for each of the movers and shakers of the Old World. Ulthuan, in particular, we should strive to get a more complete understanding of prior to our eventual trip.
Sciences and Arts
Agriculture +4 - Extensive Imperial / Extensive Dwarven
Anatomy +9 - Extensive and Esoteric Imperial / Extensive Bretonnian / Extensive Dwarven
Architecture +4 - Extensive Imperial / Extensive Dwarven
Chemistry +4 - Extensive Imperial / Extensive Dwarven
Engineering +7 - Extensive Imperial / Extensive and Esoteric Skaven (T)
Geography +4 - Extensive Imperial / Extensive Dwarven
Linguistics +11 - Extensive and Esoteric Imperial / Extensive Bretonnian / Extensive and Antiquarian Dwarven
Mathematics +4 - Extensive Imperial / Extensive Dwarven
Trade +7 - Extensive and Esoteric Imperial / Extensive Dwarven
For the most part, I'm pretty satisfied with the topics Mathilde's Library covers here - the only real addition is Mathematics, which I think is probably just a good idea in general. We know Math comes up a decent amount in spellcasting, and it's also relevant to a ton of other projects Mathilde will be working on in the future. It's in her interests to be able to reference how exactly a certain formula goes easily.
Other than that, I'd mostly like to fill out the topics already present with Imperial texts on the subject - a second perspective will be very helpful in a lot of those fields, and it makes the library more useful for people to use if they don't read Khazilid.
Geography
The Old World +6 - Extensive Imperial / Extensive Bretonnian / Extensive Dwarven
Araby +4 - Extensive Imperial / Extensive Dwarven
Cathay +6 - Imperial / Extensive and Esoteric Cathayan (T)
Ind +4 - Extensive Imperial / Extensive Dwarven
The Dark Lands +3 - Imperial / Extensive Dwarven
Dragon Isles +1 - Dwarven
Mountains of Mourn +3 - Imperial / Extensive Dwarven
Most of this category will probably get filled out as things come up - I could see us shifting to Lustrian info if a trip there started to seem more likely, for example. But for our current purposes, the main thing I'd like to see is a more broad reference section on Old World geography, some Imperial writings on Cathay to put the translated documents into context, and some references on the primary areas the K8P trading route will be headed.
Flora and Fauna
Arthropods +7 - Extensive and Esoteric Imperial / Extensive Dwarven
Canines +5 - Extensive and Esoteric
Dragons +6 - Extensive Imperial / Extensive Bretonnian / Extensive Dwarven
Felines + 6 - Extensive Imperial / Extensive Bretonnian / Extensive Dwarven
Fungi + 4 - Extensive Imperial / Extensive Dwarven
Rodents and Mustelids +5 - Imperial / Extensive and Antiquarian Skaven
Venoms +7 - Extensive and Esoteric Imperial / Extensive Dwarven
Mathilde's got references on dogs, and she's got references on rats, but she really should fill in the gap in her library and pick up some books on her god's chosen animals. Not many other things for Mathilde to add to here - Flora is more Panoramia's ballywick, and we've already got what we need for the We. I'll make an exception for Fungi, though - given the greenskin connection and the general prevelance of fungi in dwarfholds, it seems like something a Loremaster's library should have references on.
War and Combat
Greatswords +7 - Extensive and Esoteric Imperial / Extensive Brettonian
Logistics +5 - Extensive Imperial / Extensive Dwarven / Skaven
Tactics +5 - Extensive Imperial / Extensive Dwarven / Skaven
It's amusing to imagine Mathilde's only references on logistics and tactics being what she stole from the Skaven, but insofar as this category exists, it should really be filled out with Imperial and Dwarven references, to include some hopefullly less... back-stabby ideas.
Gods and Divinity
Taal, God of Beasts and Brooks +2 -Extensive
Rhya, Goddess of Nature and Nurture +2 - Extensive
Ulric, God of Winter and Wolves +2 - Extensive
Morr, God of Death and Dreams +2 - Extensive
Verena, Goddess of Integrity and Intellect +2 - Extensive
Shallya, Goddess of Mercy and Medicine +2 - Extensive
Myrmidia, Goddess of Strategy and Strength +2 - Extensive
Ranald, God of Trickery and Thieves +2 - Extensive
Ursun, God of Bears and Brawn +2 - Extensive
The Lady of The Lake, Goddess of Bretonnia +2 - Extensive Bretonnian
Valaya, Ancestor Goddess of Home and Healing +2 - Extensive Dwarven
Grungni, Ancestor God of Mining and Masonry +2 - Extensive Dwarven
Grimnir, Ancestor God of Warriors and Wounds +2 - Extensive Dwarven
Morgrim, Ancestor God of Engineers +1 - Dwarven
Smednir, Ancestor God of Ore +1 - Dwarven
Thungni, Ancestor God of Runesmiths +1 - Dwarven
Gazul, Ancestor God of the Underearth +2 - Extensive Dwarven
Let's be honest - our divinity section is pitiful. We don't even have documents on the vast majority of the various gods the Undumgi follow, to say nothing of not having info on our patron's fellow pantheon. And it's a poor loremaster that doesn't have at least basic texts available on the various Dwarven ancestor gods.