Patients will have their white blood cells removed and grown in culture under conditions to make dendritic cells. Dendritic cells are a small group of cells that belong to the white blood cell population. These cells are responsible for letting the immune system know that something foreign, like bacteria or a tumor, is in the body. Dendritic cells help the body ward off disease by alerting the immune system. In previous clinical trials, brain tumor cells called astrocytoma tumor cells and glioblastoma tumor cells were taken from the tumor that was removed during surgery. The brain tumor cells were then placed into a solution in the laboratory that made them grow. Certain parts of the brain tumor's proteins (peptides) were removed from the growing tumor cells and mixed together with the dendritic cells in the blood taken from a vein. This combination of dendritic cells and brain tumor peptides were injected into the patient's skin, like a vaccination. This process is similar to that used in vaccinations. The patients were given three and four injections of dendritic cells mixed with the tumor peptides over the course of a twenty-eight day period.