Patients will receive a series of four vaccines given weekly during the Induction phase, followed by vaccinations every 8 weeks during the Maintenance phase for as long as patients remain on the study or until the vaccine supply is depleted. In addition to the investigative treatment, patients with newly diagnosed glioblastoma will receive standard temozolomide chemotherapy and radiation treatment, with the Induction phase beginning at the conclusion of radiation. Patients with recurrent glioblastoma will not receive treatment other than the investigative treatment, unless they were previously treated with bevacizumab, in which case they will be allowed to continue receiving bevacizumab.