Can someone explain the sequence of events in 'Primer'?

Primer is a very complex movie and hard-to-impossible to understand in the first watching. This is due to the fact that we only see a small part of the actual happenings in the story, and the scenes are not in a chronologically correct order.

This is hard to spot, as the scenes seem to fit after each other, but sometimes they are reruns of a scene that is replayed by time travelling older versions of the characters, thus resulting in strange behaviour or dialogues.

One thing to look out for is the earpiece Aaron is wearing in some of the scenes. The Aaron from the future has recorded all earlier conversations, travelled back in time, replaced his earlier self and tries to recreate the dialogues this way, sometimes failing (e.g. in the basketball scene, where he misses the throw). So every time you see an earpiece, you know that this scene is not in chronological order.

I would recommend reading this very good essay, studying the timeline posted in OddCore's answer, and then rewatching the movie once or twice. It helped me understand the movie to a point where I can more or less tell what is going on.

Here you go. A picture depicting the 9 different timelines of the movie :)

The easiest explanation I have yet found of Primer can be found in an article on a sci-fi/astronomy site:

1. Inventors Aaron and Abe try to develop technology capable of making the mass of objects lighter by blocking gravity, but instead inadvertently invent a time machine.

2. Abe then builds a time machine big enough to hold a human being, and successfully proves time travel exists by going back to earlier that day. However, a person can only travel back in time as far as when the machine was activated, and one must stay inside the machine for the length of time one wishes to travel to the past, thus placing a limit on the amount of time travelling you can do.

3. In secret, Abe also construct a “failsafe” machine which in the event of something going seriously wrong he could use to reset the timeline. The “failsafe” basically allows him to travel back to a time before he discussed the subject of time travel with Aaron. Abe would then be able to sabotage the machine as many times as necessary to get Abe and Aaron to abandon their time travel efforts.

4. Over the next couple of days, Aaron and Abe travel back in time and make money investing in stocks. There is also an unfortunate incident at a party in which a shooting occurs, and Thomas Granger (Abe’s girlfriend’s father) apparently finds and uses the time machine, but becomes sick and ends up in coma. (A possible explanation could involve Granger traveling back to stop his daughter being shot by her ex-boyfriend at the party)

5. Realizing the dangers of time travel, Abe decides to use the “fail-safe” time machine and after traveling four days in the past he meets Aaron, and collapses. In a twist, Abe them discovers that his fail-safe did not seem to work and that the Aaron he meets is actually an Aaron from the future.

6. It turns out that Aaron knew about Abe’s failsafe box, and used it to take another foldable time machine back and create a “near-failsafe” point farther back than Abe’s, whilst creating a “false-failsafe” point” for Abe’s time box. (Aaron wanted to keep using the machine).

7. Aaron has used this twice in an attempt to set right the incident at the party, which he feels he indirectly caused. The problem with going back in time to “fix” things, though, is that the original copy of themselves are walking around in that timeline. To resolve that problem, whenever Abe or Aaron independently travel back to change events, they drug and render the earlier versions of themselves unconscious, before hiding them out of the way while they complete their task.

8. In the end there turns out to be 3 Aarons (2 Abes) in this universe, the timeline of which involves the original Aaron1 being drugged by a future Aaron2, who then stowed him in the attic before Aaron2 is himself later drugged by Aaron3 who, like Aaron2, had also traveled back through time. Furthermore, Aaron uses a tape-recorder to record all his conversations, and with his earpiece is able to keep his interactions in the past virtually identical, whilst only influencing those things he wants to change.

9. Eventually, Abe2 and Aaron3 team up to fix the problem at the party, after which they part in anger and in effect are enemies. Abe2 then destroys the time machine, so that it can never be used by Aaron1 and Abe1 to time travel, and experience its realities. However, Aaron2, the film’s narrator, feels guilty about having locked Aaron1 in the attic and phones him to relate the experiences of himself (Aaron2) and Aarons3.

10. The movie ends with Abe2 warning off Aaron3 at the airport, and a scene in which Aaron3 is inside a huge hanger in another country, perhaps there to build a larger version of the time machine for an extended stay. Alternatively, it could be Aaron1 having being filled in with the details of time travel by Aaron2.