This study is for adults, ages 18 to 65, who have been diagnosed with Autism Spectrum Disorder and have symptoms of Major Depressive Disorder. The treatment used will be Transcranial Magnetic Stimulation (TMS), a non-invasive form of brain stimulation that is FDA-approved for treating depression in adults. The investigators aim to treat participants' depressive symptoms and also study the possible positive impact of TMS on Autism symptoms and irritability associated with autism. In addition, the investigators will obtain imaging studies of the participants to learn more about the impact of TMS on the brain's structure and function in adult subjects with Autism. This is an open-label pilot study, meaning that each participant will receive the same treatment and that there is no 'placebo' treatment given for any of the study participants.