• Safety and tolerability of this therapy [ Time Frame: From initiation of study drug to 28 days after the end of treatment visit ]
  Number of participants with treatment-related adverse events as assessed by CTCAE version 5.0
• Objective radiographic response (ORR) [ Time Frame: Up to 2 years ]
  measured by modified Response Assessment in Neuro-Oncology (RANO) criteria.
• Progression Free Survival [ Time Frame: Up to 2 years ]
  defined as the time from date of enrollment until the earliest date of disease progression (as determined by modified RANO criteria) or death due to any cause
• Overall Survival [ Time Frame: From date of enrollment until the date of first documented progression or date of death from any cause, whichever came first, assessed up to 5 years ]
  defined as the time from date of enrollment until death from any cause

Primary Objective:

• To determine the efficacy of abemaciclib for recurrent oligodendroglioma, as measured by the estimated proportion of patients alive without disease progression at 6 months from study enrollment (PFS-6)

Secondary Objectives:

• To evaluate the safety and tolerability of abemaciclib in recurrent oligodendroglioma
• To estimate the objective radiographic response rate (ORR) associated with abemaciclib in recurrent oligodendroglioma
• To determine the median progression-free survival (PFS) and overall survival (OS) of patients with recurrent oligodendroglioma treated with abemaciclib
• To determine ORR, PFS, and OS in the subgroup of recurrent oligodendroglioma patients with tumor CIC gene mutations

Exploratory Objectives:

• To measure pharmacodynamic markers of abemaciclib activity on oligodendroglial tumor cells
• To identify pre-treatment tumor characteristics that are associated with response to abemaciclib recurrent oligodendroglioma

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.