The film begins with a young woman having her eye cut by a razor. While gruesome and an example of abject horror, it could also symbolize the barrier between the Id and the Superego, since it is only the rules and social trappings that we have created ourselves that prevents us from freely killing each other. It is also interesting to see how our educated minds prevent us from doing such a thing, though it would only take a minor lapse into the unconscious to lead into cutting someone so violently.
There are also several scenes of people looking out of windows at other scenes outside. This could symbolize people's voyeuristic nature by highlighting the way windows are a portal to the outside world and into someones personal life, with the glass acting as a social barrier, making it acceptable.
In one scene a man suddenly starts groping a young woman without warning while having visions of her naked. This obviously connotes the more animalistic side of ourselves that run on instinct. When he tries to pursue the woman, he is seen being pulled back and chained to pianos, dead horses, stone tablets and priests. This symbolizes the culture and religion of our world holding such animalistic desires back, keeping them in check.
Another scene shows an oddly dressed man having his clothes ripped away from him from what seems like a father figure. This could symbolise someones sexual identity and how people are forced to stay in there chosen identities by their peers. Later the man acquires a book which transforms into a gun. The book could represent knowledge and the gun the power that comes from that knowledge. The man uses this gun to shoot down the father figure, who then appears in an empty field, perhaps representing an afterlife. The odd clothes later appear in a small box, possibly symbolizing the secrets we keep hidden away from the general public.
Un Chien Andalou is a very odd film that jumps around in time and has little to no plot. However this can be attributed to it's initial subject of dreams and the surrealist nature of its creators. It's odd structure can also be forgiven for the time it was created in, where standard film structure hadn't really been established yet.