Canon AE-1 shutter releases when film advance lever is activated

SOURCE: I have an Canon AE-1 and the film advance lever

The film is either at the end or stuck. The shutter will not release unless the film advance lever has gone all the way and back.
Make a note of the frame counter. Rewind the film and remove it from the camera (When you feel the film to come loose from the receiving spool, stop rewinding to prevent the end of the film to disappear inside the can. This way you can reload it if it was stuck in the middle.) If the film was completely exposed, take it to be developed.
With the empty camera, try to advance the lever and release the shutter. If this works, the problem was the film and not the camera. Everything is fine. If the problem persists, take it to be repaired.
If the film was stuck in the middle, load it again into the camera. With the lense cap on (preferably in a dark room or similar) 'shoot' as many 'empty' frames as you had on the counter plus two more. Finish the film and develop the pictures.
If the film stucks again at the same place, rewind it and develop normally. It was a bad film.
Hope this helped you to solve the problem.

SOURCE: Advance lever is stuck. I

Like all AE-1's and related models, your camera is gumming up inside as the internal lubricant films are at least 25 years old and are largely dried-out.

The fix is to get the camera to a repair specialist for a CLA service (Clean, Lubricate, Adjust). As a one-off extra cost also get the foam light seals and foam mirror buffer replaced as they'll either be absent by now or will still be turning to a sticky goo. Modern foam is is different material and is will not decay like the old stuff.

A CLA and foam replacement definitely costs more than the residual value of the camera, but they're solidly built and have plenty of cheap high quality lenses so can still achieve results which compare well to even the best modern pro dSLR's. Get the work done and your camera will probably last until 35mm film ceases to be available. Your camera will also withstand conditions which you'd never dare risk a dSLR in.