Inclusion Criteria:

          1. Histologically and molecularly confirmed diagnosis of oligodendroglioma according to
             2016 WHO Classification (tumor tissue must show co-deletion of chromosomes 1p and 19q,
             referred to as "1p/19q codeletion").

          2. Oligodendroglioma must be progressive or recurrent following BOTH a) prior radiation
             therapy and b) at least one prior line of alkylating chemotherapy.

          3. Patients may have had treatment for an unlimited number of prior relapses.. Recent
             surgical resection for recurrence is allowed, as long as there remains measurable
             contrast-enhancing disease after surgery.

          4. Patients must have recovered from severe toxicity of prior therapy. Patients who
             received chemotherapy must have recovered (Common Terminology Criteria for Adverse
             Events [CTCAE v. 5.0] Grade ≤1) from the acute effects of chemotherapy except for
             residual alopecia or grade 2 peripheral neuropathy prior to enrollment. The following
             intervals from previous treatments are required to be eligible:

               -  12 weeks from the completion of radiation

               -  6 weeks from a nitrosourea cytotoxic chemotherapy

               -  3 weeks from a non-nitrosourea cytotoxic chemotherapy

               -  4 weeks from any investigational (not Food and Drug Administration [FDA]-approved
                  for oligodendroglioma or other gliomas) agents

          5. Patients must be able to swallow oral medications

          6. Age 18 or older

          7. Karnofsky performance status >= 60

          8. Life expectancy >3 months

          9. Adequate hematologic parameters, including:

               -  Absolute neutrophil count >= 1,500/ul

               -  Platelets >= 100,000/ul

               -  Hemoglobin >= 8 g/dl. Patients may receive erythrocyte transfusions to achieve
                  this hemoglobin level at the discretion of the investigator. Initial treatment
                  must not begin earlier than the day after the erythrocyte transfusion.

         10. Adequate hepatic function within 7 days prior to enrollment, defined as follows

               -  Total bilirubin ≤ 1.5 x ULN (patients with Gilbert's Syndrome with a total
                  bilirubin ≤ 2.0 mg/dl and direct bilirubin within normal limits are permitted)

               -  ALT and AST ≤ 3x upper limit of normal (ULN)

         11. Adequate renal function within 7 days prior to enrollment, defined as follows:

               -  serum creatinine <=1.5 x institutional ULN OR calculated creatinine clearance
                  (glomerular filtration rate can also be used in place of creatinine or CrCl) >=50
                  mL/min for subjects with creatinine levels >1.5x institutional ULN

        Exclusion Criteria:

        Any of the following would exclude the subject from participation in the study:

          1. Prior treatment with a CDK4/6 inhibitor

          2. Patients must not be on enzyme-inducing anti-epileptic drugs (EIAEDs; carbamazepine,
             phenytoin, and phenobarbitol)

          3. The patient has serious preexisting medical condition(s) that would preclude
             participation in this study (for example, interstitial lung disease, severe dyspnea at
             rest or requiring oxygen therapy, history of major surgical resection involving the
             stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis or a
             preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea)

          4. Females who are pregnant or lactating are excluded.

               -  If a female of childbearing potential, must have a negative serum pregnancy test
                  within 7 days of the first dose of abemaciclib and agree to use a medically
                  approved contraceptive method during the treatment period and for 3 months
                  following the last dose of abemaciclib.

               -  If a male, agree to use a reliable method of birth control and to not donate
                  sperm during the treatment period and for at least 3 months following the last
                  dose of abemaciclib.

               -  Contraceptive methods may include an intrauterine device [IUD] or barrier method.
                  If condoms are used as a barrier method, a spermicidal agent should be added as a
                  double barrier protection.

               -  Women must agree not to breast feed while on abemaciclib treatment and for at
                  least three months following the last dose of study therapy.

          5. The patient has active bacterial infection (requiring intravenous [IV] antibiotics at
             time of initiating study treatment), fungal infection, or detectable viral infection
             (such as known human immunodeficiency virus positivity or with known active hepatitis
             B or C). Patients with known HIV infection are excluded given the potential for
             interactions between antiretroviral agents and abemaciclib. Patients with known
             Hepatitis B or Hepatitis C infection are excluded only if there is evidence of active
             infection (detectable Hepatitis B surface antigen, detectable Hepatitis C RNA). For
             patients without known viral hepatitis or HIV infection, viral hepatitis and HIV
             testing are NOT required to determine eligibility for this trial.

          6. The patient has a personal history of any of the following conditions: syncope of
             cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but
             not limited to, ventricular tachycardia and ventricular fibrillation), or sudden
             cardiac arrest.

          7. Subjects with major medical, neurologic or psychiatric condition who are judged as
             unable to fully comply with study therapy or assessments should not be enrolled.

          8. Prisoners or subjects who are involuntarily incarcerated are excluded.

          9. Subjects who are compulsorily detained for treatment of either a psychiatric or
             physical (eg, infectious disease) illness are excluded

         10. Subjects requiring concurrent administration of any other anticancer agents including
             chemotherapy and biologic agents (such as bevacizumab) or the use of other concurrent
             investigational treatment drugs and/or devices.