Disclaimer: If I mention other systems, it's as a generalization and mostly for if the reader is unaware what is "normal" for a magical system to do. It's not meant as a poke at other systems. Secondly, there might be some topics I might not get into verbose detail just to keep this short enough to read (or else I'll end up writing War and Peace). This is going to be long enough as it is. If you want further details, ask. I'm skipping over swathes of info to keep this reasonable.
Energy Manipulation, Magical senses, "Tech", Analysis, Research, and Information sharing are the basis of Omnimancy as a tradition. Each play an important role in supporting the others, and in the end all improve each other and support each other, which continues the cycle of advancement. This is over generalizing of course, but it breaks down to that.
The basics of Omnimancy are based on movement/shaping of "magical" energy and the ability to see/sense what you (and others) are doing with said energy(Energy Manipulation). Magical senses are a cornerstone of the system, since being able to see what you're doing and what others are doing is very important. One is expected to be able to do analysis on not only your own spells but others and you can't do that without a means of observation. With observation comes confirmation, meaning, if you do something, it's important to have your peers review it to make sure you did what you thought(if such a review is reasonably possible). In this case, you wouldn't say anymore than that you did something and perhaps the general place to "look". The whole point is for the peers to figure out what you did and if they all came up with what you did, then you have outside confirmation, if not, then we see WHY it doesn't match up. Outside confirmation is a serious confidence booster. But that is group dynamics rather than the system, so let's get back to that.
"Tech" is one of the hardest things to explain, however it is what gives Omnimancy its power/abilities over simple raw will. "Tech" is short for Technology and Technique.
Raw will is the most common means of performing magic. Meaning, using one's will alone, you gather energy, shape it(if that's what you do), put intent into it (which gives it its function), and then set it in motion. Now this may be done using focuses or other techniques, and in many cases in ritual, this is how it breaks down if the casting is being done by the practitioners versus contacting another entity to do the casting for them.
In Omnimancy, the first part of gathering energy is streamlined so it takes but a few seconds or less depending and can still yield a great amount of energy. In the majority of cases in ritual, one would gather energy into oneself or at least donate from one's own energy into the ritual. This is a time consuming process depending on your style/method. We generally discourage using one's own energy or bringing energy into oneself to be used for spell work (for many reasons). Normally, to make ambient magical energy useful, it needs to be gathered and compressed to increase it's density (think of compressing an energy ball, which is common, or drawing energy into oneself which in the process increases it's density simply by packing it inside oneself). If one is pulling from personal energy, it's already dense enough to be used. At low levels, we would tap into a local ley line, which is already dense energy. This would consist of simply connecting a "hose" to it which we call a tether(which is a spell itself) and letting the energy flow down it. Ley lines usually have a back pressure so no pumping is needed. A spell can be created from either gathering local energy and compressing it to be used for spell work(which is common in rituals when energy is "raised"), or energy from the tether can be used directly. Once created, the spell is made to take energy FROM the energy in the tether rather than powering itself off the caster, as well as grow larger from the excess energy. This does two things. First, very little personal energy was used to manipulate this energy into operation(the act of using will uses some but almost negligible amount of personal energy). The new spell is NOT being powered off the caster as is normal, but an outside source as not to drain the casters reserves of power which he uses to wield his magical power in the first place. The end benefit is this kind of spell working can be done repeatedly virtually without wearing out the caster at all. Second, the amount of "spare" energy for the spell from a ley line is normally at least double(much more in most cases) than what a caster would normally spare to power the spell if he was powering it. Since the spell is made to grow more powerful with the excess energy, it does. So what you end up with by a simple technique is an individual caster that can cast more powerful than normal spells many times without getting worn out.
Tech in a spell's construction(Technology) is defined as a series of parts that make up the whole to a final goal. Meaning, a car has many parts made of different materials, all doing one thing individually, but arranged in such a way that as a whole make a motor vehicle greater than the sum of it's parts, and used (in the case of a car) to transport many hundreds of pounds at high velocity. Tech works the same way. Normally, a raw will spell will be "neutral" or at least uniform energy with intent. In a computer analogy, if one thinks of "intent" as a software program, telling the spell what it should do, tech would be specialized hardware to do the same goal or similar more efficiently. In raw will spells, the hardware is simply the energy itself. In a tech spell, there are quite literally parts arranged in such a way that perform a task VERY efficiently for what it's constructed for. Meaning, with little power, it can do a lot, which also means, with a lot of power, it can do that much more.
A good analogy to give this idea more meaning is to think of wanting to dig a hole in your backyard for a pool. There are many methods to that end goal, each with their pros and cons. Think of raw will as just using your hands to dig in the dirt. It works, but it's slow, and the only way to make it more efficient is to grow stronger. There is also a concept called a construct, which is shaped energy for a task which is common in certain magical systems. The equivalent here would be a shovel. A shovel is a single part basic machine but is far more efficient than digging with your hands. It can be made more efficient with minor tweaks, but those tweaks are limited, as well as it is still greatly dependent on the strength of the wielder. So after the tweaking is over, all that can be done to make things better is to make the wielder stronger. In Tech's case, it would be like using a back-hoe. The operator ends up moving some levers which activates the machinery and hydraulics to move this big claw and creates that pool hole REAL quick with minimum effort on the operator's part. Tweaks can be done on MANY parts of the machine, such as better metals for strength, a better engine, etc. However, what were required to make it were many disciplines of combustion, metallurgy, hydraulics, and other forms of engineering. How all of this would relate back to a spell is that a tech based spell would have systems (much like the back-hoe has it's electrical system, it's hydraulic system, it's combustion system, etc.), and within those systems are parts, and those parts are made of particular materials with specific properties best suited for the purpose of the part itself. Those individual parts could be considered constructs, or sometimes the material itself is mini-constructs, to get the properties needed over normal uniform raw will energy. Now obviously, one isn't making something as complex as a back hoe off the bat, but things get that complicated eventually in the system higher up. Fortunately, it's much easier to actually USE the system than it is to explain it. Much of the complexity hangs out more in the background of the caster than foreground of what he has to keep track of. If the caster WISHES to view and understand the complexity, he only has to look closer at the spell itself, so most of the complexity becomes more second nature. What is also interesting is you can pull parts and systems out of a spell to make something completely different. Much like you could pull a lot off the back hoe and make a big go cart or whatever.
This is where information sharing comes into play, because in many cases, other people will look at the "problem" of the back hoe and replace parts with more efficient parts of things that they have either come across or invented themselves. Different people's minds work differently, and will notice things that others might skip. Also, people's interests are different, so one might spend more time on tech involving power, or materials or whatever suits the person's fancy. The point is, they bring their discoveries back to the group and everyone swaps in a big tech trade (more common at "research" level), so now the others have the same abilities as the one who invented it and vice versa. Even if it's all based on the same original concepts, people will take it various directions. The one GOOD thing about tech is that it's 100% transferable (at least via our current methods, there was a problem early on but was solved). There is no longer the problem of individual X is the only one able to do Y because it's innate, and while they might be able to teach it, the receiver never seems to be able to do it as well. That problem is common in many systems. However, further innovations are of course going to be more easily made by the originator than the receiver, but that's progress of the individual. Sometimes others simply come up with things that take combinations that others simply didn't think of. The permutations are almost endless. Again, fortunately in practicality, much of the details don't NEED to be known by the conscious mind unless it wants to, otherwise it would be completely unwieldy. If something is complex and needs to be done manually, it only needs to be done once because you can tell yourself to "do it again", or even "do it again" but modify "*this*". This latter technique allows one to have the benefit of years of tweaks without having to start from scratch each time (we refer to it as macro casting).
Another major part of what we do is analysis. Not only on spells(not only ours but other magical system's spells as well) and how they are constructed and work, but on techniques also. We also do spiritual biological analysis as well, determining how a spirit works to a certain extent (and the universe/multi-verse around us for that matter). It's very complex, however some parts are more obvious than others. We have found, for example where one's senses are located and how they function(to a point), as well as the "hardware" within the spirit that allows it to transform it's own thought/will into controlling magical energy (i.e. exerting their magical will on outside reality). From understanding how the spirit is able to manipulate magical energy, we have learned to take advantage of that and create amplifiers to enhance that ability. Many revisions and different techniques have been used over the years, some straight forward, others out of a genetic scientist's nightmares(which worked the best actually). I've shown the low to mid-end amplifiers to many other mages of various systems over they years and they were impressed by the results.
So the analysis basically allows us to understand how things work, and then we research ways of using that knowledge to our advantage to make things more powerful, more effective and more efficient. With the extra magical will the amplifiers allow, it makes things much easier/quicker as well as eventually allowing us to do things that an individual would normally not be able to do. They also normally increase ones magical senses so much more detail is noticed, which helps with the research. By using these methods, the individual trained mage in Omnimancy, by being able to cast very powerful/complex spells quickly, and in rapid succession on demand with no implements other than themselves without wearing themselves out.
Well, that's the magical system/tradition in a generalized nutshell. The training normally takes 18-24 months(minimum at the time of this writing) these days with at least two new unique topics each week. Some people can handle that, others can't. It's purposely meant to be quick so that the student is then able to teach but also mostly able to help out with relevant research. Many students start their own research long before they hit research level, and those are the ones that normally do the best.