So, did you already see Donnie Darko and still don't get? then take a look at this post

 I think its more than clear that the post itself is a spoiler, but hey, if you already saw the movie then go ahead and read. (if you did not see the movie what are youdoing by reading this?)  

   
The truth is that this film can have several interpretations, if you do not want to spend too much time trying to understand the movie you can stay with the fact that Donnie is a delirious schizophrenic, who is flashing everything or that everything is a dream, on the other hand if you follow the thread of history Roberta Sparrow's book "philosophy of time travel" practically explains everything, you just have to follow through.

The universes     

I think it's best to start by explaining the difference between universes.  
The primary universe is our universe, it is the universe we see, reality, this is a stable universe, but it can be affected by the tangent universe. The tangent universe is an unstable version of the primary universe, as an alternate reality, but it can only be sustained for a few weeks after it collapses upon itself creating a black hole in the primary universe capable of destroying all existence.

   
The story takes place in the primary universe until the night Donnie leaves his room and meets Frank on the golf course. At that moment we enter the tangent universe, where Donnie evades his death by not being in his bed the moment a plane turbine falls into his room.

When Frank tells Donnie that the world ends in a little more than 28 days, it means that at that time collapsed the tangent universe.

 The artifact     

Usually the first indication that a tangent universe has occurred is the emergence of an "artifact". The artifact is an element that enters the universe seemingly out of nowhere, creating a tangent universe, in this case the artifact is the airplane turbine, and if the artifact is not returned to the primary universe all existence would be destroyed.
 

The work of returning the artifact falls to Donnie because he is the "living receiver" and Frank acts as a guide in this task because he falls into the category of "manipulated dead"

The living receiver 

    

The living receiver is chosen to guide the artifact into position for its journey back to the primary universe. No one knows how or why a receiver will be chosen. The living receiver is often plagued by terrifying dreams, visions and auditory hallucinations during his time in the Tangent Universe.
 

The living receiver is often blessed with dimensional powers. These include increased strength, telekinesis, and the ability to evoke fire and water.
 

- increase in strength when an ax is stuck in the bronze statue
- ability to evoke water when he floods the school
- ability to evoke fire when Cunningham's house burns  - telekinesis when the artifact returns to the primary universe

The manipulated living 

 Often the manipulated living are close friends and neighbors of the living receiver.
They are prone to irrational, extravagant and often violent behavior. This is the unfortunate result of his task, which is to assist the living receiver in returning the artifact to the primary universe.
The Manipulated will do anything to save themselves from oblivion.
 

The manipulated  dead   

 
 

The manipulated dead are more powerful than the living receiver. If a person dies within the Tangent universe, they are able to contact the living receiver through the Fourth Dimension Construction.
 

The manipulated dead will manipulate the living receiver using the Fourth Dimension Construction. They will establish an assurance trap for the live receiver, to ensure that the device is safely returned to the Primary Universe.

If the ensuring trap succeeds, the living receiver is left with no choice but to use its dimensional power to send the artifact back in time into the primary universe before the Black hole collapses on itself.
 

"They made me do it" 

    

Throughout the movie everyone is unconsciously trying to help Donnie, that's why all the echos are related forming a chain of events that takes us to the final arc of the story.

Frank first tells Donnie to flood the school

So he can meet Gretchen on the way home

Also because he flooded the school, Mrs. Farmer tries to apply the philosophy of Jim Cunningham 

      

What ends in the discussion for the line of love and fear

       

So she calls on Jim Cunningham for a conference at the school  

     

Then Donnie ends up hating him and burning his house   

    

Thanks to that it is discovered that Jim was a pedophile    

   

Which causes Mrs. Farmer to lead the campaign in her defense and Donnie's mother goes on a trip with Samantha  

     

That's why Donnie and Elisabeth can throw a party  

 

What gives way to the final events of history   (which would prove to be the "safe trap")

This is when Frank runs over Gretchen and Donnie shoots Frank.

       

Getting to the end of the tangent universe Donnie has to accept his destiny to save everyone    

        

"You are a product of fear"

   
Donnie is afraid of dying and more by dying alone. If the artifact returns to the primary universe he knows that he will die, because Frank does not wake him, because it is not an element of the primary universe.
 

 It's only a few hours before the tangent universe collapses.   At this point, the important thing is that Gretchen dies and her death is what motivates Donnie to return the artifact, not to save the universe, but to save her, which showed the beauty of life and gives it the value to accept his death.  

 The philosophy of time travel also explains that the key elements for time travel are metal and water.
 

Water is the barrier element for the construction of time portals used as passage between universes like the tangent vortex.
 

Metal is the transition element for shipbuilding of artifacts.
The artifacts are formed from metal, like an arrowhead from an ancient Mayan civilization, or a metal sword from medieval Europe.

    
The turbine is the metal echo artifact and construction of the fourth dimension is made of water
Donnie counts on these two elements when he uses his dimensional power to detach the turbine from the plane and makes his journey in time.

   
Then Donnie sends the artifact back to the primary universe back in time, while awake in his bed laughing as if everything had been a dream.
In the end Donnie dies sleeping when the turbine falls on him. 

 

Usually people always have the same question each time I explain this theory, so I shall explain it in the following content.       

Why does Frank save Donnie at the beginning of the movie if he will die anyway? 

  The fact is that from the moment Frank starts interacting with Donnie events take place in the tangent universe, if Frank lets Donnie die at first, Donnie would be dying within the tangent universe, remember that Donnie's job as a living receiver is of sending the artifact (the turbine) to the primary universe, otherwise the universe itself would’ve collapsed.   

Frank has to save Donnie within the tangent universe so that he can fulfill his function as a living receiver and be able to avoid the destruction of the universes.