Travis Bickle (Robert De Niro)’s Timeline and Summary

Travis gets a job at the taxi company so he can drive around at night instead of passively suffering insomnia.
He develops a crush on Betsy, who works on the campaign for presidential candidate Charles Palantine.
Acting on a misguided first date idea, Travis takes Betsy to a porn movie. She definitively rejects him.
Travis starts to go crazier and crazier. He buys a full arsenal of guns and fantasizes about violence.
He shoots a robber who was attempting to hold up a corner store. The store owner beats the robber's half-living body and Travis leaves.
Travis tries to convince a twelve year old prostitute, Iris, to leave her pimp and find a better life elsewhere, but she won't say that she'll go.
Sporting a new Mohawk, Travis almost tries to assassinate Charles Palantine, but he's spotted when attempting to draw his gun. He flees successfully.
Instead of killing Palantine, he murders Iris' pimp, Sport, and two other gangster-ish guys. Travis is wounded and then tries to kill himself, but is out of ammo.
While in a coma from his wounds, Travis is hailed as a hero and thanked by Iris' parents.
Back at work as a taxi driver, he gives Betsy a free ride in his cab, and drives off into the night, his future unknown.