Dose Escalation Study to Determine the Safety of IFN-Beta Gene Transfer in the Treatment of Grade III & Grade IV Gliomas

Inclusion Criteria: 1. Must be greater than or equal to 18 years of age. 2. Subjects must have histologically proven GBM, AA, AMO, malignant astrocytoma NOS or gliosarcoma and recurrent or progressive tumor following prior treatment. 3. Tumor must be amenable to radical resection, and resection must be clinically indicated. 4. Must have an ECOG performance status of 0-2. 5. Must be on anticonvulsant therapy, and must have therapeutic serum levels within 2 weeks prior to Day 1, if therapeutic levels are defined for the anticonvulsant being used. Exclusion Criteria: 1. Abnormal blood tests exceeding any of the limits defined below: * Alanine transaminase (ALT) \> four times (4X) the upper limit of normal (ULN). * Aspartate transaminase (AST) \> 4X the ULN. * Total bilirubin \>1.5 mg/dL. * Absolute neutrophil count \<1,500 cells/mm3. * Platelet count \<100,000 cells/mm3. * Serum creatinine \>2X ULN. * Prothrombin time (PT) \>2 seconds above the ULN. * Serum sodium (Na) \<125 mEq/L or \>150 mEq/L. * Serum potassium (K) \<3.5 mEq/L or \> 5.5 mEq/L. 2. Brainstem, or optic chiasm involvement of tumor. 3. Uncontrolled seizure disorder. 4. History of a new diagnosis or treatment of an invasive malignancy other than Grade III or Grade IV Glioma within 5 years of enrollment. Curatively treated subjects with a history of basal cell or squamous cell carcinoma of the skin, superficial transitional cell carcinoma of the bladder, and non-invasive carcinoma of the uterine cervix are not excluded. Treatment History: 5. Treatment with radiation therapy, including interstitial radiation or radiosurgery, must be completed at least 8 weeks prior to Day 1. 6. Treatment with nitrosoureas must be completed at least 6 weeks prior to Day 1. Treatment with other chemotherapeutic agents must be completed at least 4 weeks prior to Day 1. 7. Treatment with any investigational drug or approved therapy for investigational use must be completed at least 4 weeks prior to Day 1. 8. History of intolerance to corticosteroids that would preclude use during this study, or history of any medical condition that precludes the use of corticosteroids. 9. Any prior treatment with a gene delivery vector, or an adenovirus therapeutic. 10. Women of child bearing potential must have a negative serum pregnancy test. 11. Women who are not postmenopausal, surgically sterile, or willing to practice effective contraception during the study. Men who are not surgically sterile or willing to practice effective contraception during the study. 12. Nursing mothers, pregnant women and women planning to become pregnant while on study. 13. Previous treatment with BG00001.