-  INCLUSION CRITERIA:

          -  Patients must have a clinical diagnosis of NF1, i.e., patients must have at least two
             of the diagnostic criteria for NF1 listed below (NIH Consensus conference) or a
             confirmed

        NF1 mutation from a CLIA-certified laboratory:

        -- Six or more cafe-au-lait macules (>= 0.5cm in prepubertal subjects or >= 1.5 cm

        in post pubertal subjects)

          -  Freckling in axilla or groin

          -  A neurofibroma or plexiform neurofibroma

          -  Optic glioma

          -  Two or more Lisch nodules

          -  A distinctive bony lesion (dysplasia of the sphenoid bone or dysplasia or thinning of
             long bone cortex)

          -  A first-degree relative with NF1

               -  Presence of >= 1 ANF (biopsy confirmed) for whom surgical removal could cause
                  significant clinical morbidity OR for which patient is unwilling to undergo
                  surgical resection OR the presence of more than one distinct nodular lesion (DNL)
                  including at least 1 biopsy proven ANF

        NOTES: Definition of DNL. In addition, there will not be a requirement for confirmed
        CDKN2A/B deletion for study eligibility due to known biopsy sampling error and tumor
        heterogeneity.

          -  Age >= 12 years old (no maximum age) with associated age-related requirements as
             follows:

          -  Age >= 12 years old with BSA >= 0.71 M^2 and able to swallow whole tablets

          -  Willingness of patients >= 12 years old and <18 years old to undergo pre-treatment
             percutaneous biopsy of ANF if deemed feasible with minimal morbidity

          -  Willingness of patients >=18 years old to undergo pre-treatment and on-treatment
             percutaneous biopsy of ANF if deemed feasible with minimal morbidity

        NOTE: For patients of all ages with ANF that cannot be safely biopsied with minimal
        morbidity, biopsy requirement to be performed at NIH Clinical Center will be waived from
        eligibility criteria. In this case, review of available archival tissue by NIH Pathology
        will be necessary to confirm diagnosis of ANF, which is mandatory for eligibility.

          -  Measurable disease: Patients must have at least one measurable ANF defined as a lesion
             of at least 3 centimeters (cm) measured in one dimension. Measurability and
             suitability for volumetric MRI analysis of the target ANF must be confirmed with the
             NCI POB prior to enrolling a patient. The target ANF will be defined as the clinically
             most relevant ANF, which has to be amenable to volumetric MRI analysis.

             - Prior Therapies:

          -  Since there is no standard effective chemotherapy for patients with NF1 and ANF,
             patients may be treated on this trial without having received prior medical therapy
             directed at their ANF.

          -  Investigational agents/biologic therapies (not chemotherapy): Patients who have
             received previous investigational agents or biologic therapies are eligible for
             enrollment. At least 28 days must have elapsed since receiving medical therapy
             directed at any NF1 related tumor. Patients who received prior medical therapy for a
             NF1 related tumor manifestation must have recovered from the acute toxic effects of
             all prior therapy to <= grade 1 CTCAEv5 except for residual alopecia or Grade 2

        peripheral neuropathy prior to enrollment before entering this study.

          -  Chemotherapy agents: Patients who received chemotherapy must have recovered (CTCAE
             Grade <=1) from the acute effects of chemotherapy except for residual alopecia or
             Grade 2 peripheral neuropathy prior to enrollment. A washout period of at least 28
             days is required between last chemotherapy dose and enrollment (provided the patient
             did not receive radiotherapy).

          -  Patients who received adjuvant radiotherapy must have completed and fully recovered
             from the acute effects of radiotherapy. Patients who have received previous radiation
             therapy are eligible for enrollment. At least 6 weeks must have elapsed since the last
             radiation therapy and start of treatment. The only target ANF cannot have received
             radiation previously.

          -  At least 4 weeks must have elapsed since any major surgeries, with evidence of good
             wound healing. Minimally invasive biopsies and central line placements are not
             considered major surgeries.

          -  Patients who have received prior treatment with abemaciclib or another specific CDK4/6
             inhibitor are not eligible for enrollment

               -  Adequate performance scale (Lansky/Karnofsky >=70%).

               -  Adequate organ function as defined below:

          -  Hematologic Function: Patients must have an absolute neutrophil count =1500/ micro
             lliter, hemoglobin >=9 g/dL (transfusion independent, defined as not receiving blood
             transfusion unless related to trauma or surgeries), and platelets >=100,000/ micro
             liter (transfusion independent, defined as not receiving platelet transfusions unless
             related to trauma or surgeries)

          -  Hepatic Function: Patients 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: Patients must have a creatinine clearance or radioisotope GFR
             >=60ml/min/1.73 m^2 or a normal serum creatinine based on age, described below.

          -  Age (years) is >12 and <=15 then Maximum Serum Creatinine (mg/dL) = 1.2

          -  Age (years) is >15 then Maximum Serum Creatinine (mg/dL) = 1.5

          -  Cardiac Function: Normal ejection fraction (ECHO or cardiac MRI) >= 53% (or the
             institutional normal; if a range is given then the upper value of the range will be
             used); QTC or QTcF <=450 msec.

               -  Willingness to avoid grapefruit or grapefruit juice during abemaciclib
                  administration

               -  Informed Consent: Ability of subject or Legally Authorized Representative (LAR)
                  to understand and the willingness to sign a written informed consent document.
                  All patients or their legal guardians (if the patient is < 18 years old) must
                  sign an IRB-approved document of informed consent to demonstrate their
                  understanding of the investigational nature and the risks of this study before
                  any protocol-related studies are performed. When appropriate, pediatric subjects
                  will be included in all discussions.

               -  Based on animal studies, the effects of abemaciclib can cause fetal harm. For
                  these reasons, women of child-bearing potential and men must agree to use a
                  highly effective contraceptive method during treatment and for at least 3 months
                  after the last dose of abemaciclib. 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, and 4 months after completion of abemaciclib
                  administration

          -  Woman subjects of childbearing potential (WOCBP) must have a negative serum pregnancy
             test with a sensitivity of at least 25 mIU/mL within 7 days of the first dose of
             abemaciclib.

          -  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).

          -  Contraceptive methods may include intrauterine devices (IUD), or barrier method, a
             spermicidal agent should be added as a double barrier protection.

          -  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
             outcomes and breastfeeding are to be collected for regulatory reporting and drug
             safety evaluation.

        EXCLUSION CRITERIA:

          -  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.

          -  May not have a NF1-related tumor such as optic pathway glioma or malignant peripheral
             nerve sheath tumor, which requires treatment with chemotherapy or surgery.

          -  Serious preexisting medical condition(s) that would preclude participation in this
             study (for example, interstitial lung disease, severe dyspnea at rest requiring oxygen
             therapy, 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 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]. Patients 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.

          -  Patients with interstitial lung disease

          -  Requires treatment with strong CYP3A inhibitors or inducers

          -  Inability to swallow tablets, since tablets cannot be crushed or broken.

          -  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 volumetric analysis of target ANF on MRI.

          -  Refractory nausea and vomiting that would limit drug administration in the opinion of
             the Principal Investigator

          -  Known severe hypersensitivity to abemaciclib or any excipient of abemaciclib or
             history of allergic reactions attributed to compounds of similar chemical or biologic
             composition to abemaciclib

          -  Clinical judgment by the investigator that the patient should not participate in the
             study