* INCLUSION CRITERIA:
* Participants must have recurrent high grade glioma or midline glioma based on clinical and/or radiologic findings
* Participants with cortical high grade gliomas must have previous intra-operative pathology confirming disease
* Participants must be \>= 18 and \<= 39 years old at the time of enrollment
* Ability to swallow tablets/pills
Prior Therapies:
* At least 4 weeks must have elapsed since any major surgeries, with no evidence of infections. Minimally invasive biopsies (outside of the brainstem) and central line placements are not considered major surgeries
* Participants who have received prior treatment with abemaciclib or another specific CDK4/6 inhibitor are not eligible for enrollment (ex., Ribociclib, Palbociclib - list is not all inclusive)
* Participants who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events \[CTCAE\] Grade \<=1) from the acute effects of chemotherapy except for residual alopecia or Grade 2 peripheral neuropathy prior to treatment. A washout period of at least 14 days or 4 half-lives from last disease directed therapy, whichever is shorter, is required between last chemotherapy dose and treatment.
* Participants who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 14 days is required between end of radiotherapy and treatment.
* Adequate performance scale as defined below:
* Karnofsky \>=50% within 14 days prior to enrollment.
* Adequate organ function within 14 days prior to enrollment as defined below:
Hematologic Function: Participants must have an absolute neutrophil count \>=1500/microliters, hemoglobin \>=9 g/dL (transfusion independent, defined as not receiving blood transfusion unless related to trauma or surgeries), and platelets \>=100,000/microliters (transfusion independent, defined as not receiving platelet transfusions unless related to trauma or surgeries)
Hepatic Function: Participants must have bilirubin within 1.5 x the upper limit of normal for age, with the exception of those with Gilbert syndrome, and AST/ALT within \< 3 x upper limit of normal.
Renal Function: Participants must have a creatinine clearance or radioisotope GFR \>60ml/min/1.73 m2 or a normal serum creatinine.
Cardiac Function: Normal ejection fraction (ECHO or cardiac MRI) \>= 53% (or the institutional normal); QTC or QTcF \< 450 msec.
* Willingness to avoid grapefruit or grapefruit juice during abemaciclib administration
* Informed Consent: Ability of participant or Legally Authorized Representative (LAR) to understand and the willingness to sign a written informed consent document.
* Willingness of participant or LAR to sign a written informed consent document and co-enroll in study 03-N-0164
* The effects of abemaciclib on the developing human fetus are unknown, however CDK-inhibiting agents are known to be teratogenic. Temozolomide is a cytotoxic chemotherapeutic agent which is known to be teratogenic. For these reasons, women of child-bearing potential must agree to use a highly effective method of contraception prior to study entry, for the duration of study participation, and for 3 weeks after the last dose of abemaciclib and 6 months after temozolomide. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation.
* A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus).
* Woman participants of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 7 days of the first dose of abemaciclib.
Highly effective contraception include intrauterine devices (IUD), hormonal (birth control pills, injections, implants), tubal ligation, or partner s vasectomy .
--Cases of pregnancy that occur during maternal exposures to abemaciclib should be reported. If a participant or spouse/partner is determined to be pregnant following abemaciclib initiation she must discontinue treatment immediately. Data on fetal outcomes and breastfeeding are to be collected for regulatory reporting and drug safety evaluation.
-Abemaciclib administration must be able to begin no later than 14 days after the date of radiographic diagnosis (by T2 or FLAIR imaging)
EXCLUSION CRITERIA:
* Participants who cannot safely undergo a biopsy due to contraindications
* Pregnant women, or women who intent to become pregnant during the study, are excluded from this study because of the teratogenic effects of abemaciclib. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with these agents, breastfeeding should be discontinued if the mother is treated on study.
* Serious preexisting medical condition(s) that would preclude participation in this study (for example, interstitial lung disease, severe dyspnea at rest requiring oxygen therapy, severe renal impairment \[e.g. estimated creatinine clearance \<30ml/min\], history of major surgical resection involving the stomach or small bowel that would preclude adequate absorption, or preexisting Crohn s disease or ulcerative colitis or a preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea).
* Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, active bleeding diatheses or renal transplant, or psychiatric illness/social situations that would limit compliance with study requirements.
* 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.
* Active systemic 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 \[for example, hepatitis B surface antigen positive\]. Participants with HIV who have adequate CD4 counts and who have no requirement for antiviral therapy will be eligible. NOTE: Screening is not required for enrollment.
* Requires treatment with strong/moderate CYP3A inhibitors or inducers. Participants receiving any medications or substances that are inducers or strong/moderate inhibitors of CYP3A4 are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the participant will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering a new over-the-counter medicine or herbal product.
* Inability to undergo MRI and/or contraindication for MRI examinations following the MRI protocol (see Study Procedure Manual). Prosthesis or orthopedic or dental braces that would interfere with MRI.
* Refractory nausea and vomiting that would limit drug administration in the opinion of the Principal Investigator
* Known severe hypersensitivity to abemaciclib, temozolomide or any excipient of abemaciclib or temozolomide or history of allergic reactions attributed to compounds of similar chemical or biologic composition to abemaciclib and temozolomide.
* Clinical judgment by the investigator that the participant should not participate in the study
