Travis Bickle is one of our most richly layered psychos. His initial state is that of an honorably discharged veteran. Throughout the film, we see him slowly descend into madness due to insomnia, obsession and the effect of the violence and depravity around him.
Travis is an observer. We see that from the very first few shots of him in the film, a close up of just his eyes. He keeps a journal of his observations, mostly about the “scum” he witnesses every day while driving his taxi. Oddly enough, he sees himself as apart from this perverse world of drug dealers, hookers, and con men, though he himself is a regular frequenter of porn cinemas. He even takes his obsession Betsy to a Swedish sex education film showing he doesn’t really have a grasp on what IS acceptable behavior which calls his criticisms into question.
I’d like to link this to his journal. It’s a technique used by many writers. The literary term is Epistolary and it means a narrative told in document form, be it letters, newspaper articles, journal entries, etc. Travis’s journal also provides the film with its voice-over narration which is a means to hear the character’s inner most thoughts. This is also a characteristic of a noir style of filmmaking.
Some more famous epistolary novels include:
Dracula, The Color Purple, The Screwtape Letters, Carrie, Bridget Jones’ Diary, The Perks of Being a Wallflower, and We Need to Talk about Kevin (an amazingly powerful novel) just to name a few of my favorites. This form transcends the novel as well. One can imagine that the whole franchise of Star Trek is an epistolary form in that each episode begins with someone speaking a Star Date Log entry.