Are there mechanics for writing books that can teach multiple topics? For example if my Magus wanted to write a book that is both a Tractatus on Mentem and a Summa of Philosophy (talking about the "human mind" chapter in A&A, how do I calculate the time needed for writing? Can I choose that the book can actually be studied from twice?
In canon there are books on multiple topics. There is no advantage to it, though, as they're just treated as multiple different books attached to each other. So, for example, if they were two separate books, one person could study Dominion Lore while another studies Islamic Law, but to do so with a single copy of The Qu'ran (level 5, quality 10 summa on each) would not be possible. There are examples of combined tractatuses and summas (e.g. The Bible) and combined tractatuses (e.g. The Talmud). A single source can also be composed of several books, essentially just binding the larger book in smaller sections, too. I don't believe any mechanic is ever offered that would make it beneficial for the writer to write a single book that works as several books, though; it's just a little less expensive for the buyer of a mundane book.
The only real advantage I could think of is in the 'extras' if you're using the more expanded library rules. You only have to deal with one book if you're trying to clarify the book, or use resonant materials. If you're writing a commentary tractatus, people may only need to read through the book once, rather than once per book if it was separated. These would be probably subject to troupe opinion, of course. The final real advantage is if you're using a magical ritual to duplicate the book, CrHe(etc), you'd only need to cast the spell once to have two or three books created if they're written as a single volume.
Moving from "books on multiple topics" to just "multiple books bound together", there are also Florilegia (Covenants pg 90) - bound together groups of tractatus on the same subject which get a quality bonus from the resonance with the surrounding texts. They explicitly can't currently be further enhanced by the use of resonant materials.
I think allowing Summae and Tracti on multiple topics in a single text makes sense & is an interesting idea. Suppose the author of a Tractus determines their source quality will be ten overall; they should be able to allocate 'My Tractus will grant 5 points in Profession:Scribe, and 5 points in Magic Theory'; a student spends one season studying, and gets those points. Extra points of Source Quality from Good Teacher are allocated by the author when the book is written; extra points of Source Quality from 'Book Learner' are allocated by the student -- maybe with the restriction of equal or fewer additional Source Quality points than the author provides.
This seems like a wash to me; the same number of points are learned in a season.
Summae might be treated similarly, but the author's highest Source Quality would be restricted by whatever included subject has the poorest (maximum -- but the author could choose to write to a lesser level) Source Quality; each subject may have different levels, but again the total Quality of all subjects added together cannot exceed the maximum quality the author could write on a single subject. Or some similar restriction along those lines, as agreed by the troupe.
I think it would be fun to include a Quality 15 Level 1 Summae of 'All Hermetic Arts', for example. An apprentice who has just had their Arts opened can go from zero to one in every Art in one season, enough to allow learning very basic 'apprentice level' spells in each specialty.
It should be L5Q15 but books along these lines already exist in canon and are exceptionally cheap. Mentioned in Covenants as Roots or Primers. The I generally think of roots as L6Q21-ish while primers are the weaker ones.
I said Level 1, because that is the maximum level attainable by studying the book; the student gains 15 points from reading the book (thus Quality 15), but each point is in a different Art. For purposes of trade & costs, it probably ought to considered higher level. A standard Level 5 Quality 15 summae would take a student from level zero to level 5 in a single Art in a season of study, which is different from what I wish to accomplish.
The exact stats of Roots and Branches (and Primers, Covenants pg 91) are left undefined; but the multi-Art summae I propose above would obviously be a primer. It could also be done as a Tractus (again, Quality 15) which grants exactly one point in each of the fifteen Arts -- it would then provide at least some minimal benefit to post-Gauntlet magi.
It's already RAW that distractions reduce the Advancement total (Core, p. 165), so I don't really see how it wouldn't be possible to, say, study from 4 different summae in one single season, each detracting from the study of the other. Indeed, I usually houserule that this is possible.
For example, you could read The Analects of Tytalus (House Tytalus Lore Summa, L4Q11 + Philosophiae Summa L3Q11 + Order of Hermes Lore Tractatus Q8) and gain 11* 1/3 XP in Tytalus Lore (I usually round this down to 3) and 11*2/3 XP in Philosophiae (also rounded down, to 7) in the same season. Rounding down helps avoiding abuse and diminishes bookeeping. You could also read and gain 5XP in Philosophiae and 4XP in OoH Lore (it adds a bit of bookeeping to tractatus but I don't think it's much, honestly; the maximum amount of XP you can get from any one tractatus doesn't change, it's capped at the original Quality).
This way there is no weird interaction with Study Bonus or Book Learner (since these virtues add to the Source Quality, not to the Advancement, and the SQ is proportionally divided).
Writing is also straightforward. Writing a compound summa is written in the same way that a regular summa, but you must finish everything to have a complete book (so if your Com+Language total is 7 you need 6 seasons to write the Analects, 5 for the summae part and one for the tratactus part).
As for a L1Q15 summa on all Arts it seems indeed interesting, but also a bit useless? The difference it would make for an apprentice is almost zero (you go from TeFo 0 to TeFo 2, hardly a game changer to cast 1st magnitude spells).
You've got to be really careful chopping up summas this way because there are actually some really weird interactions written into the original core rules here, including with things like Book Learner. I'll give a quickly example to showcase it, once with and once without Book Learner.
You study 6 Quality-12 summas that are all well above your level, for 2 weeks apiece.
Without Book Learner:
You gain 12/3=4 experience in each of 6 areas, for a total of 24 experience. (Notice the big boost.)
With Book Learner:
You gain (12+3)/3=5 experience in each of 6 areas, for a total of 30 experience. (Notice increased bonus from Book Learner.)
However, the problem was fixed with this erratum, allowing only one book:
It would be 12/6 w/o book learner if you divided it proportionally, 2 XP each.
With book learner, (12+3)/6 = 2.5 (I would round this down, exactly to avoid this being exploited and becoming total 18 XP).
What I'm suggesting is that there is no difference in the total XP gained IF it remains proportional to the actual time you spend reading over that season. I'm against mixing different types of advancement, I think it's a necessary abstraction. But as long it's only books? To me it's fair play.
But nice call on the errata, I wasn't aware.
EDIT: Within reasonable limits, of course. I don't think it is reasonable to study, say, from 90 different books in one season, one day each, potentially gaining XP in 90 different areas. I use this as a simple way to solve that couple of XP missing somewhere (you are short 6XP to Creo 6 and there is a L10Q12 summa available? Yeah, you can read for half the season and pick another summa with the rest of the time, no problem). It's not game breaking, but neither is it usually necessary, or even desirable.
Sure, but that's not what the distraction rules on p.165 say. They say each book loses 2/3 of the Advancement Total, which is calculated after Book Learner is included. That's why I was warning against using the distraction rules you cited in this way.
If you do it all proportionally and round fractions down, you shouldn't run into problems.