First let me say thank you for putting this out there, I apologize that a lot of what you are about to read will be more critical, but at least you are trying and put forth a significant amount of time and energy into this.
So glancing through quickly there is a fair share of language translation issues I think making it more difficult to read, not bad, but in a technical document these become much more of an issue.
That being said, you are kind of all over the place for an ‘introductory’ document, jumping into more advanced math (As in math I never even studied and would have a hard time understanding) at the start, then going back to cover absolute basics of how we hear or what type of microphone is what, etc. I wouldn’t worry about trying to explain acoustics for instance, until I described how sound acted in a space and how we hear it. The math behind a fourier transform is not necessary to understand enough of how analog to digital conversion works for 90% of audio work for instance, not really an introductory topic for sound technology, more DSP introduction topic there, and DSPs themselves can be a more advanced topic for sound.
I also have to mention you have some lack of understanding in some areas, for instance I can jump to areas I know pretty well, and point out some errors in what you did write, which is likely more detail than needed, while skipping more basic topics. ie.:
The classical form of radio wave transmission uses frequency modulation (FM). To improve the signal to noise ratio it uses a 1:2 compression in the transmitter and a reverse expander in the receiver. This may lead to artefacts that may disturb in extremely demanding applications.
Companders in analog FM transmission are usually not quite as simple as a 1:2 compressor and expander, which is why when you use systems from one manufacturer with another manufacturer, the sound quality will be very wrong. In fact Lectrosonics, a higher end manufacturer of wireless microphones, has created multiple emulations to allow for use of other manufacturer’s microphones with their receivers to account for the differences. Honestly you don’t need to go into how the expansion and compression works here, other than to identify it exists, again identifying the ‘basic’ level of introduction needed to cover a topic. Of course for a basic level of introduction on the topic of wireless microphones at all you get into topics you didn’t address such as intermodulation (Or existing/other users of common spectrum, or differences between spectrum, etc.) so it may be better to just remove this section all together, especially because in order to truly understand it requires a knowledge of the laws of the country you are in, instead of just understanding the physics behind it.
Glancing through the live sound section, your advice on the whole isn’t bad, but it is just advice, and missing basic information. Rather than advice people to use DIs and emulation(Which almost never flies professionally), you need to think about why that amp or cabinet should be mic’d, or ways that sound can be controlled from it (You allude to this earlier with acrylic sheets, but don’t go into much detail with examples of why, which this can be a great one).
Another example of giving examples without touching to much on the thought process behind them:
10.5.1 Minimal Solution, no Bass
A very basic setup for signals with little bass (speech, small acoustic instruments) can be done with two small loudspeakers on stands on each side of the stage. One single central loudspeaker would either stand in the way between artist(s) and audience or behind the stage at the worst place for the danger of feedback.
Most of the time if you are doing a smaller setup, it is actually preferable to use a single speaker. While you are correct in that a single speaker behind the performer can lead to feedback or be visually disruptive, very often one speaker set to the side of the performer is enough to provide coverage needed, and since most of a smaller setup is going to be in mono anyways, actually provides a clearer coverage as producing a mono mix in two speakers both covering the same area will lead to phase cancellation and a loss of clarity compared to a single reproduction source.
You description of arrays for live sound is primarily incorrect honestly. The important aspect to them is using the fact the LF drivers are arranged to be mounted very close together, not that they can be mounted with a 5 deg angle. This allows for summing, and through the fact that audio has a travel time, the delay creates a natural phase cancellation and summation at frequencies dependant on the length of the array to provide more directionality than would be experienced by a single driver, and to replicate in a horn requires a very large horn. However due to physics this often doesn’t translate to HF sound, which is in turn guided by other means (Waveguides etc.) in arrays, which is why the hybrid curved array became popular as opposed to the constant curvature described in your document, as you could focus HF sound to where it was needed better than a constant curve. Of course all of this results in phase smearing in the HF compared to single carefully controlled drivers, but the tradeoff is often considered worth it for many cases (Though not all).
Similar problem with your description of cardioid subs, which are generally arrays of drivers, not a single driver with a hole in the rear of the box (Which sounds more like a typical ported sub honestly). Time delay and phase/polarity is used to create zones of summation and cancellation given the travel time of audio at specific frequencies.
I haven’t had time to read the entire document, and again let me state that I am appreciative that you are willing to do this. I had something similar on a Drupal site once for my classes but lost it when the database was corrupted, and haven’t ever gone back to recreate it since, I just don’t have time, so I do understand how much an investment of time and effort this was. I just think that some focus on specific introductory topics may bring out strength to your document, and leave some of the other topics out for a different document.