It can be difficult to comb through terms and conditions to understand airline policies. Here is a summary of the key points of American Airlines' flight cancellation policy:
All tickets: Can be canceled for a full refund within 24 hours of purchase if booked at least two days before departure.
Refundable tickets: can be canceled for a full refund by requesting a refund online or by contacting reservations.
Non-refundable tickets: no refund after the 24-hour grace period. However, if you cancel a flight prior to departure, you can apply the unused value of eligible fares toward future travel, provided the new flight is within one year of the original ticket issuance date.

Currently, you can only make changes to your trip once.

Note that this policy only applies to purchases made directly with American Airlines. If you bought your ticket from a travel agent or on a website, you must contact the travel agent directly.