The Guilds primary function was more or less to allow everyone relative easy access to magical services and equipment when necessary, and whether or not each individual hall enforces anything...well, yeah. The simplest spells are easy enough to grasp for children, so depending on local, I doubt that anyone that dabbles in magic must indicate that they have some level of Guild training. This is also assuming that any Guild Hall ever enforced its own edicts, which seems to be something that varies on a regional basis.

As for independent groups like Winterhold, well...

This is the best we can do. Given that Synod still operated to some extent in former Mages Guild Halls, I do think it stands to reason that there were independent institutions of magical learning regardless of its existence.

The College of Winterhold also predates the Mages Guild.

Well, date of establishment is semi-irrelevant, since it is possible that they could theoretically acknowledge to the Guilds authority at any given date. Still, I think its safe to say that there are independent organizations that existed along side the Mages Guild regardless of its authority. Running around and crushing things it doesn't like never fell into the Guilds focus (Trebonius now withstanding), and probably wouldn't take any type action against external forces unless something went horribly wrong. I mean hell, the Psiijics still had emissaries around during the period, and the Guild never went after them.

He says "The guild can provide you with some training," meaning other training can be found outside of the guild. He then goes on to say "but the best trainers are usually very hard to find." This implies that that the "best trainers" are not connected to the guild and the "some training" that the guild provides. It seems very clear....

The fact that the only two people who ever mention him (one being a guild member) both seem to have no real clue of who he is, where he is, or at all what he is like, indicates that he isn't being kept track of or regulated by anyone, including the guild. Of course the guild could be keeping track of him and he could be affiliated with them, but there is absolutely no dialogue or really any evidence to suppose that this is the case. If anything, when Litte says "I personally wouldn't go looking for him myself" this gives us reason to think that he might actually be a dangerous person. It is also possible, as you say, that he is practicing and training illegally and the guild just doesn't want to put in the effort to go and arrest or kill him; but why would Alberic Litte, an advanced conjuration trainer and guild member tell you that you can go and receive training from him if it is illegal to do so? Is it really more reasonable to believe that he is somehow sanctioned by or a member of the guild even though there is no evidence to show this? Or is it more reasonable to simply say that he is a self taught mage practicing on his own and teaching people legally?

I am not sure what you mean by this. All I am saying is that alchemy is a part of the magical arts as evidenced by the fact that the Mages Guild, who's chief purpose is to provide magical services to the public, sells alchemical ingredients and potions. I have never seen the Mages Guild provide any non magical services to the public.

No I wouldn't know that they are all part of a society if I had never played the Unfriendly Competition quest and it would be odd of me to assume that they were involved in some society if the quest didn't exist. But since the quest does exist, we have direct evidence that such a society exists and are thus justified in believing in it.

You are advancing the claim that the Mages Guild has total control over who practices magic and in what fashion. The only direct evidence you have provided to suppose that this is true is the Unsactioned Training quest, which PrinceSchroob provided a reasonable alternative explanation for. You also cited the Recruit or Kill Llarar Bereloth quest in which the same woman asks you to kill a member of house Telvanni. But by your own admission, the Telvanni would be exempt from the Mages Guild's control over magic, so even you must admit that her actions in this second quest are illegal, thus adding to PrinceSchroob's claim that she is acting illegally in the first quest as well. The only other evidence you have is that it is never directly stated that the various trainers and mages I listed aren't members of the guild (though the case of Olyn Seran basically does state this).

In short, it requires fewer assumptions to believe that mages are allowed to learn magic on their own rather than make the leap and assume that every mage is either affiliated with the guild or is a criminal.

Outside of guild services. That doesn't mean those trainers aren't affiliated with or sanctioned by the guild, just that it's not official guild services.

I wouldn't put much stock in how only a couple NPCs mention him. For one, Oblivion had a low number of topics per NPC, and the first use of fully voiced NPCs meant that few of them could talk about specific things. Further, finding the master trainers is not supposed to be easy, so you wouldn't want everyone talking about them.

In Daggerfall, the Mages Guild offered access to a Library, and offered training in various languages (like Dragonish, Orcish, etc). Like alchemy, these things would no doubt be useful to mages, but that doesn't mean they're inherently magical.

And we have reason to assume trainers are involved with the guild, either by being members or being sanctioned/licensed by them. Both in the way the MG throws its weight around with stopping/killing non-guild trainers and practitioners, and how their charter explicitly says they establish laws regarding the proper use of magic. It's telling that the vast majority of magic users that are known or strongly presumed to not be affiliated with the guild are either outlaws, hermits far from civilization, part of a group that could give the MG a run for its money (the Telvanni, Psijics), or employed directly by the Empire. The only real question I have is about The College of Winterhold, which apparently was unaffiliated with the MG in the 3rd Era. Was the College that much of a powerhouse that the MG didn't want to tangle with them? Was the Empire giving them special permissions about magic training?

Both, possibly. Winterhold by the late third era was famous enough to attract a very sizable number of Dunmeri immigrants due in large part of the College, who actually does not have magical services open for public use like the Mages Guild is supposed to. We do know that the Imperial Battlemage has a great deal of authority when it comes to magic in general, so it is plausible to go through the proper channels and get their approval to operate independently. There's also, again, the Blackcasters in Hammerfell in a city that is largely based on magical knowledge and what not, and IIRC had won itself autonomy from the Empire on par with Morrowind after the treaty of Stros M'Kai. No telling what other groups could very easily exist out there, so long as they the proper approval.

I think this depends wholly on who the head of the Hall is in a specific region, and whether or not they particularly deem it necessary to enforce its edicts. Ranis for instance comes down extraordinarily hard on those outside of the Guild practicing magic, having you either forcibly recruit or kill people outside of the Guild on a regular basis throughout her quests. Meanwhile you have unaffiliated people like http://www.uesp.net/wiki/Morrowind:Leles_Birianthat offers spell crafting, which is noted as being more particularly dangerous in universe, but is never touched upon at all. The Legion also offers magical training detached from the Guild.

So the question is, was the Mages guild a unilateral power that enforced its own edicts everywhere with heavy hand, regardless of location, or was this part of it sporadic and wholly dependent on who is running the show in each Guild Hall? Strikes me that the latter is far more realistic to expect then the prior, especially since the Empires stance on it for the most part is seemingly "Sort if out yourselves." in this regard.

The latter makes more sense to me as well. People like Ranis would leverage such power more than, say, Jeanne Frasoric.

In the context of Necromancy, though, it seemed to be a rather high-profile issue within the guild, with the Archmage himself being fervently against it, so I doubt many of the guild hall chapters could let it go on openly for long even if they wanted to.

Well, I dunno about that. It certainly won't be on record of course, but if a leader of one of the Guild halls is extremely lenient and in a particularly far flung location, they might actually be able to get away with that. I mean, certainly before Oblivion came around, the likes of Ulliceta gra-Kogg probably operated and generally ignored it so long as it wasn't too depraved or obvious. No say on how the Order of the Lamp, which we know very little about, would react. Probably not well, I'm guessing.

Given that the Guild shattered into the Synod and College of Whispers respectively, I think it says a lot about how the Mages guild in reality conducted itself and what policies each person decided to enforce or ignore. Though, I don't remember any word on the College of Whispers and whether or not it was a officially sanctioned organization by the 4th era empire.

Perhaps, but I'd think it's very unlikely. The general opinion on necromancy isn't very positive, so odds are that eventually someone within a guild hall would complain if their local guild hall leader let it go on openly. Some letters to the AU would then easily ensure such a leader is quickly relieved of their position.

Depends on how insular it is. Necromancy in Elsweyr and Orsinium is supposedly fairly common, so the likelihood that anyone within the confines of a Hall is would raise alarm is significantly reduced if its kept local. They're not going to run around and raise dead in the streets naturally, but most likely in private practice off the record. You get caught, you take the fall and all that, if someone doesn't off you before hand. And if someone doesn't like something...peer pressure is a nasty and very real thing, and if applied...well, y'know. The number of members that defected from the Guild after Travens crack down on the practice was quite significant if I'm not mistaken. That does say it had a very strong presence in the Guild, even if it was done so illegally, to say nothing of regions in Tamriel where necromancy is not entirely frowned upon like it is in Morrowind or Cyrodiil.

It's not even illegal in Cyrodiil either, just because the Mages Guild frowns upon it doesn't mean it's been made officially illegal by the Empire which furthers my belief that what Traven is doing with his little witch-hunt can be seen as illegal.

Yes, mage guild has an somewhat monopoly on teaching spells, however tempels can also do this, same with telvanni both might be grandfatered in.

You had spell shops in Oblivion imperial city but this was probably under mage guild it was very public and let them keep the university area for members only.

Lots of the high level traners was probably mages fed up by the policy and power games in the guild many was also very involved in their own projects.

it looks like studying at least at an mage guild for some time was pretty common and did not result in you spending your entire life in the guild.

Reason for controlling training in magic would be similar to modern arms control, making it harder for someone to raise an army of batlemages. Yes such an system if full of holes but it work better than no control.

Perhaps the Vigilants of Stendarr aren't legal. They are generally only encountered in the wilderness, and the only time I can recall (off the top of my head) seeing a Vigilant in a city was when he was breaking into a house. They don't really have a big presence (or any presence, really) in civilized places. Any examples of Vigilant presence in cities (that doesn't involve illegal activities)?

Also I'm assuming that the Vigilants of Stendarr are distinct from typical worshipers of Stendarr, as there are certainly Stendarr acolytes and supporters in the cities.

That's why I think they are only tolerated in skyrim because of a mutual hatred for daedra and stuff like that otherwise in the other provinces they're not as well off.

Nah. With the exception of Morrowind, nearly any and all places that aren't smack dab in the middle of the wilderness generally consider Daedra being a bad thing. The Nords aren't that great of a deviation from the norm regarding them.

Eh, depends. High Rock is the most versatile in religions from what we know so far from Daggerfall (though I guess we can debate that nowadays) and Cyrodiil has always been the home of numerous cults and religions. Bosmer probably don't care, Khajiit worship Azura as Azurah and Argonia is probably closed off to outsiders. So it's probably just Skyrim and Hammerfell.