(Manta is the energy found within your Trigger which is an organ found attached to the right side of the heart of every sentient being. In its raw form Manta is pure spiritual and life energy however, it can be twisted and manipulated with to create various techniques and abilities. Depending on the amount of manta you have in your Trigger and how refined your Manta is, the rank of your Trigger can increase we call these ranks "Core ranks" and the individuals able to utilise the awakened Core ability "Core users". More on Triggers and ranks later.)
(Core users can use their Manta in many different ways, this does not just include core abilities. The 3 main applications used are:
Strengthening - This technique is called Tsuyoi (強い) which literally translates to strong or potent. If you output a certain amount of Manta into your Tsuyoi, the potency of it can decrease or increase exponentially, this principal goes for all applications of Manta not just Tsuyoi. Going into more detail, Tsuyoi can be used for Defense and Offense, defense usually involves enveloping the body with Manta and creating a slight repulsive force. Offense usually consists of enveloping the body once again, but this time you Manta is in a more refined form.
Projecting -This technique is called Nageru (投げる) which translates to throw or cast. The technique involves outputting Manta outside of the body in many different ways. Healing Nageru which as the name implies can heal wounds, stabilize vitals and even reverse cellular damage. This variation is Rare and requires high life focused-Manta control. Binding/Shaping Nageru an extremely small number of Core users are able to manipulate Manta into constructs like chains, shields or tendrils.
Core Ability - The ability you gain from awakening your Trigger. There are different classes to different types of Core Abilities which will be explained further on in the story.)
I hope this'll help you understand the first few chapters better!