Inclusion Criteria:

        Cohort A specific inclusion:

          -  Histologically confirmed IDHwt, RB intact, grade II or III glioma that has recurred
             after first line therapy (consisting of at least maximum feasible surgical resection
             and radiation therapy). There is no limit on the number of prior therapies or types of
             therapies patients can have received.

          -  Measurable disease on imaging (1cm) or measurable non-enhancing tumor.

          -  At least 12 weeks elapsed since prior radiotherapy

        Cohort B specific inclusion:

          -  Patients with histologically confirmed glioma of any grade (II-IV) who are planned for
             a standard of care surgical debulking/resection and for whom participation in this
             study would not cause a medically unacceptable delay in surgery.

          -  Patients must have relapsed/progressed following therapy (consisting of at least
             maximum feasible surgical resection and radiation therapy).

        Cohort C specific Inclusion:

          -  Histologically confirmed IDH mutant glioma, meningioma, schwanomma, PCNSL, ependymoma,
             or other Primary Brain Tumors that have recurred despite previous standard of care
             therapy. Because this cohort is, in part, meant to allow patients access to therapy
             who might not otherwise be eligible for other clinical trials - deviations from
             standard of care treatment or histological confirmation can be presented to and
             approved by the Principal Investigator for inclusion in the study.

          -  Histologically confirmed PCNSL that has recurred after prior methotrexate-based
             chemotherapy or for whom methotrexate-based chemotherapy is deemed medically not in
             the patient's best interest.

        Glioma patients:

          -  Standard of care next generation sequencing via a CLIA certified platform must be
             available, or planned and at a minimum include IDH, and RB status.

        All cohorts:

          -  Patients must provide written informed consent prior to any screening procedures.

          -  Age 18 years or older.

          -  KPS ≥ 60

          -  Willing and able to comply with scheduled visits, treatment plan and laboratory tests

          -  Patient is able to swallow and retain oral medication

          -  Required baseline laboratory status:

               -  Hemoglobin > 8 g/dL (SI Units: 80 g/L). 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.

               -  Platelet count ≥ 100 x 10^9/L

               -  Absolute neutrophil count (ANC) ≥ 1.5 x 10^9/L without growth factor support

               -  Total bilirubin ≤ 1.5 x upper limit of normal (ULN)

               -  AST/SGOT and/or ALT/SGPT ≤ 3 x ULN

               -  Serum Creatinine ≤ 1.5 x ULN

          -  Stable dose of corticosteroids for > 5 days prior to baseline MRI

          -  Before starting study treatment, patients must have recovered from toxic effects of
             prior therapies (except for residual alopecia or Grade 2 peripheral neuropathy) and at
             least 3 weeks must have elapsed since any prior signaling pathway modulators, (e.g.,
             EGFR, FGFR, or other tyrosine kinase inhibitors), at least 3 weeks must have elapsed
             since temozolomide, 4 weeks must have elapsed since carboplatin or cisplatin, and at
             least 6 weeks from nitrosoureas (e.g., BCNU, CCNU). In general, at least 4 weeks must
             have elapsed from any other anticancer drug therapy (e.g. bevacizumab).

          -  Patients must be able to undergo contrast enhanced MRI scans (or contrast enhanced CT
             scans for patients unable to tolerate MRI).

          -  Patients must have shown unequivocal evidence for tumor progression by MRI (or CT for
             patients who cannot tolerate MRI) in comparison to a prior scan. The same type of
             scan, i.e., MRI (or CT for patients who cannot undergo MRI) must be used throughout
             the period of protocol treatment for tumor measurement.

          -  Life expectancy of greater than 8 weeks

          -  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.

        Note: Cases of pregnancy that occur during maternal exposures to abemaciclib should be
        reported. If a patient or spouse/partner is determined to be pregnant following abemaciclib
        initiation, she must discontinue treatment immediately. Data on fetal outcome and
        breast-feeding are collected for regulatory reporting and drug safety evaluation.

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

        Exclusion Criteria:

          -  No limit on number of prior therapies

          -  Evidence of significant intracranial hemorrhage

          -  No other investigational or standard anti-tumor therapy allowed

          -  Patients must not have a known history of allergic reactions attributed to compounds
             of similar chemical or biologic composition.

          -  Patients must not have a serious preexisting medical condition(s) or uncontrolled
             intercurrent illness 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) or psychiatric illness/social situations that
             would limit compliance with study requirements.

          -  Patients who have a personal history of any of the following conditions: syncope of
             cardiovascular etiology, ventricular arrhythmia of pathological original (including,
             but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden
             cardiac arrest.

          -  HIV-positive patients on combination antiretroviral therapy are ineligible because of
             the potential for pharmacokinetic interactions. This applies only to patients who have
             a documented history of HIV; HIV testing is not otherwise required.

          -  Have an active systemic fungal and/or known viral infection (for example, human
             immunodeficiency virus antibodies, hepatitis B surface antigen, or hepatitis C
             antibodies)

          -  Patients must not be on EIAEDs

          -  Females who are pregnant or lactating

          -  Must abstain from grapefruit juice

          -  Patients must not have other active concurrent malignancy

          -  Concurrent treatment on another clinical trial. Supportive care trials or
             non-therapeutic trials (i.e. Quality of life) are allowed.