Important Themes in Donnie Darko

• There is a strong theme of paranoia and schizophrenia throughput the film, especially characterized by a central character called Frank, a figment of Donnie's imagination (although this point is debatable, as there are often scenes were Frank materialises in the real world. It conveys the point that the main character is troubled. Another point about Frank is that he only appears in the darkness, adding to the elements of fear and the supernatural and increasing the enigmatic storyline.
• The main character has a very jovial and casual way of speaking, especially as he describes what he's done, eg in therapy; "I flooded the school, and I burned down that pervert's house" and then smiles and laughs. This means that Donnie has serious mental issues, yet he isn't particularly shaken or worried, even by Frank. However, there are scenes where Donnie's mood changes and he becomes extremely upset and distraught with the situation he's in.
• There is a strong chronological theme that ties the plot together. It is set into motion at the beginning when Donnie is told by Frank that the world will end in 28 days, 6 hours, 42 minutes and 12 seconds. At frequent points there is a countdown on the screen, giving the viewer a sense that time has passed in the film, and that the end is coming.  
• A strong supernatural theme runs throughout the film, such as the theory of time travel being constantly talked about and related to on many occasions, mainly when Donnie is introduced to it by his teacher at school. Another instance on the supernatural and science-fiction is the way of locating vectors along which people will travel, in essence seeing the future, which is utilised by Donnie near the end of the film. 
• The final point to make is that important themes and points that occur throughout the film are often left extremely unresolved, open and ambiguous. This means that important points such as the aspect of time travel, paranoia, schizophrenia and reality are intentionally left unanswered for the viewer to try and work out for themselves. It is also a clever move by the director as it leaves the viewer wondering, and therefore watching the film again and again to try and unravel the mystery left in the story. 

Donnie Darko on IMDb