Inclusion Criteria:

        Adult participants (greater than or equal to 18 years old):

          -  Histologically confirmed de novo (primary) glioblastoma with unequivocal tumor
             progression or recurrence.

          -  In case of testing at the time of first progression: either at least 3 months after
             the end of radiotherapy or have tumor progression that is clearly outside the
             radiation field or have tumor progression unequivocally proven by surgery/biopsy

          -  Absence of any psychological, familial, sociological or geographical factors
             potentially hampering compliance with the study protocol and follow-up schedule; such
             conditions should be assessed with the patient before registration in the trial.

          -  Availability of adequate biological material (formalin-fixed paraffin embedded [FFPE]
             tumor) for central testing of Epithelial Growth Factor Receptor (EGFR) amplification

          -  Presence of EGFR amplification confirmed by central assessment; participants with
             undetermined EGFR status are excluded

          -  World Health Organization (WHO) Performance status 0 - 2

          -  No more than one line of chemotherapy (concurrent and adjuvant Temozolomide based
             chemotherapy including in combination with another investigational agent is considered
             one line of chemotherapy). Chemotherapy must have been completed at least 4 weeks
             prior to randomization.

          -  Post surgery MRI within 48 hours following surgery, however an MRI scan has to be done
             within 2 weeks prior to randomization.

          -  Surgery completed at least 2 weeks before randomization and patients should have fully
             recovered as assessed by investigators.

          -  Renal function: calculated creatinine clearance ≥ 30 mL/min by the Cockcroft-Gault
             formula.

          -  Liver function: bilirubin < 1.5× upper limit of the normal range (ULN), alkaline
             phosphatase and transaminases (ASAT) < 2.5× ULN

        Pediatric sub-study participants (less than 18 years old):

          -  Histologically proven high grade glioma (HGG: WHO grade III glioma [e.g anaplastic
             astrocytoma, anaplastic oligodendroglioma, anaplastic oligoastrocytoma], grade IV
             glioma [e.g. glioblastoma, gliosarcoma] or diffuse intrinsic pontine glioma [DIPG]).

          -  Must either have recurrent/progressive tumor or, if newly diagnosed, have completed
             any planned radiation therapy at least 4 weeks prior to first dose of ABT-414.

          -  The tumor tissue must have been determined to have EGFR amplification, (by local or
             other testing service).

          -  Availability of adequate biological material for retrospective confirmatory central
             testing of EGFR amplification

          -  Participant has sufficiently recovered from previous therapy. The investigator
             believes that benefit of treating the pediatric subject with ABT-414 outweighs the
             expected risks and that this treatment is in the best interests of the pediatric
             subject.

          -  Renal function: calculated creatinine clearance ≥ 30 mL/min by the Cockcroft-Gault
             formula for pediatric patients ≥12 years of age and estimated glomerular filtration
             rate ≥ 30 mL/min/1.73 m^2 by modified Schwartz equation for pediatric patients < 12
             years of age.

          -  Liver function: Total bilirubin ≤ 1.5× upper limit of the normal range (ULN),
             Aspartate Aminotransferase (AST), and Alanine Aminotransferase (ALT) <= 3× ULN.
             Participants with Gilbert's syndrome documented in medical history may be enrolled if
             total bilirubin is < 3 times ULN. Not allowed are participants with known chronic
             liver disease and/or cirrhosis.

        Exclusion Criteria:

        Adult population (greater than or equal to 18 years old):

          -  Prior treatment with nitrosoureas

          -  Prior treatment with bevacizumab

          -  Previous exposure to Epithelial Growth Factor Receptor (EGFR) targeted agents,
             including EGFRvIII targeting agents

          -  Prior discontinuation of temozolomide chemotherapy for toxicity reasons

          -  Prior Radiation Therapy (RT) with a dose over 65 Gy to the brain, stereotactic
             radiosurgery or brachytherapy unless the recurrence is histologically proven

          -  Previous other malignancies, except for any previous malignancy which was treated with
             curative intent more than 5 years prior to randomization, and except for adequately
             controlled limited basal cell carcinoma of the skin, squamous carcinoma of the skin or
             carcinoma in situ of the cervix

          -  Women of childbearing potential must have a negative serum or urine pregnancy test
             (minimum sensitivity 25 IU/L or equivalent units of HCG) within 72 hours prior to
             randomization.

          -  No history of wheat allergies and Coeliac disease.

          -  No EIAED, patients who require anti-convulsant therapy must be taking non-enzyme
             inducing antiepileptic drugs (non-EIAED). Patients previously on EIAED must be fully
             switched to non-EIAED at least 2 weeks prior to randomization.

        Pediatric sub-study (less than 18 years old):

          -  (For recurrent disease) No prior RT with a dose over 65 Gy to the brain, stereotactic
             radiosurgery or brachytherapy unless the recurrence is histologically proven

          -  No current or recent (within 4 weeks or 5 half-lives [whichever is shorter] before
             enrollment) treatment with another investigational drug

          -  Female participants of childbearing potential must have a negative serum or urine
             pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 72
             hours prior to randomization.