The world hidden from humanity

Just like usual, I wake up and get dressed, I open the door to the hallway and go downstairs to the living room.
When I arrive downstairs I see Mochi sitting in a sofa with his legs crossed and feet on a little coffee table.
I decide to sit in the sofa opposite of him and the table, when I sit down he moves his legs and goes to a sitting position.
"Well then." he says to me "Let's get started with teaching you magic."

What followed was something of immense value as it changed my perception of the world around us.
"All magic comes from the same source, but this source is so far beyond our current understanding that we will not get there any time soon." was the start of a long monologue.
"This doesn't mean we can't tap into this source and use it's power, it just means that we can't use it to it's full potential just yet."
"As a way to work around this, two models where invented that enabled us to tap into this power and use it to modify the world around us."
"Teaching you the two systems would be useless since they can practically do the same things, they just differ as to what the base form of magic actually is."
"The system I prefer is the more powerful of the two, but it comes at the cost of being harder to learn."
"I will teach you this system because it has greater efficiency when it comes to converting mana and activating spells."

He paused for a second and took a sip from the can on the table.
After that he immediately continued with his explanation, it was quite long and tiring so I summed it up in a brief manner.

The base of classical magic lies in different elements and their ties to the objects around us.
Every object uses some base element or combination of it as it's composition.
These elements can then be boiled down into 6 primal ones, these are known as 'Aer' (Air), 'Terra' (Earth), 'Aqua' (Water), 'Ignis' (Fire), 'Ordo' (Order), 'Perditio' (Disorder).
The art of classical magic is all about using these elements to manipulate the world around us.
These primal elements can be combined into compound elements.

"I'm not gonna go into detail about compound elements as they are quite a mess if you don't understand how elements combine" Mochi told me.
He had finally finished his explanation and stood up from his chair. He then walks towards the other door in the room and signals me to follow.

While I'm walking towards the door he says "it's best to practice now so what I told you can be cemented into your head."
When I arrive Mochi had already opened the door and started signaling me to go through ahead of him.
The room on the other side is huge, it's like a gym hall but with all sorts of equipment for target training and trinkets I'm not even familiar with in the slightest.