-  INCLUSION CRITERIA:

               1. A documented deleterious germline BRCA1/2 mutation (gBRCA1/2m) obtained in a
                  CLIA-certified laboratory, including but not limited to Myriad Genetics, either
                  by multi-gene panels or individual testing, for Cohort 1 participants prior to
                  study enrollment. Participants with documented somatic BRCA mutation obtained in
                  a CLIA-certified laboratory also will be considered for Cohort 1.Variants of
                  uncertain significance (VUS) of BRCA1/2 are not considered deleterious.
                  Participants with VUS or deleterious mutation in other genes without gBRCA1/2m
                  can be considered for Cohort 2 or 3 or 5.

               2. Participants enrolling in the sporadic high grade serous epithelial or high grade
                  endometrioid ovarian cancer group, Cohort 2, must have a negative family history
                  of hereditary breast ovarian cancer (HBOC) syndrome, or negative gBRCA1/2m
                  mutation test.

               3. Participants enrolling in the triple negative breast cancer (ER-/PR-/Her2-)
                  group, Cohort 3, must have a negative family history of HBOC syndrome, or
                  negative gBRCA1/2m test. A family history of HBOC is defined by NCCN
                  Genetic/Familial High-Risk Assessment: Breast and Ovarian guideline.

               4. For Cohorts 1-3, 5 and 6: participants must have breast and/or epithelial or
                  endometrioid ovarian cancer, primary peritoneal cancer, and/or fallopian tube
                  cancer histologically or cytologically confirmed at the NCI that is metastatic or
                  unresectable and for which standard curative measures do not exist or are no
                  longer effective. ER/PR/HER2 status needs to be documented either by an outside
                  source or at NCI. Participants with gBRCA1/2m with history of or active breast
                  and ovarian cancers are considered for Cohort 1.

                  Participants enrolling in Cohort 5, the recurrent platinum-resistant sporadic
                  high grade serous epithelial or high grade endometrioid ovarian cancer group,
                  must have a negative family history of HBOC syndrome, or negative gBRCA1/2m test.
                  Participants should have recurrent platinum-resistant - defined as disease
                  recurrence by imaging within 6 months of the last receipt of platinum-based
                  chemotherapy. Rising CA125 only is not considered as platinum-resistant disease.
                  Participants with primary platinum refractory disease defined as progression
                  during or within 3 months after receiving first-line platinum based chemotherapy
                  are not eligible.

               5. All participants must have measurable disease, defined as at least one lesion
                  that can be accurately measured in at least one dimension (longest diameter to be
                  recorded for non-nodal lesions and short axis for nodal lesions) as greater than
                  or equal to 20 mm with conventional techniques or as greater than or equal to 10
                  mm with spiral CT scan.

               6. All participants except Cohort 6 must have at least one lesion deemed safe to
                  biopsy and be willing to undergo a mandatory baseline biopsy. For Cohort 5, the
                  second biopsy at progression is mandatory for the responders (PR/CR/SD) > 4
                  months.

               7. Participants enrolling in Cohort 6, the recurrent platinum-resistant sporadic
                  high grade serous epithelial or high grade endometrioid ovarian cancer group,
                  must have a negative family history of HBOC syndrome, or negative gBRCA1/2m test.
                  Participants should have recurrent platinum-resistant, defined as disease
                  recurrence by imaging within 6 months of the last receipt of platinum-based
                  chemotherapy. This cohort should have measurable (defined by RECIST v1.1) but
                  without biopsiable disease, determined by PI and Interventional Radiology (e.g.,
                  cystic abnormal mass, not safely biopsiable disease). Rising CA125 only is not
                  considered as platinum-resistant disease. Participants with primary platinum
                  refractory disease defined as progression during or within 3 months after
                  receiving first-line platinum based chemotherapy are not eligible.

               8. Participants must be at least 4 weeks from previous therapy (chemotherapy,
                  hormonal therapy, and radiation therapy, or investigational agents; 6 weeks for
                  mitomycin C).

               9. The use of raloxifene, denosumab, or bisphosphonates for bone health is allowed.

              10. There is no limit on the number of prior therapies.

              11. Participants must be at least 1 week from the last dose of complementary or
                  alternative medications.

              12. Participants who have had major surgery must be fully recovered and greater than
                  or equal to 4 weeks postoperative prior to enrolling on study.

              13. Age greater than or equal to 18 years.

              14. ECOG performance status less than or equal to 2.

              15. Participants must have normal organ and marrow function (in the absence of
                  transfusion 24 hours prior to dosing) as defined below:

                  leukocytes greater than or equal to 3,000/mcL

                  absolute neutrophil count greater than or equal to 1,500/mcL

                  platelets greater than or equal to 100,000/mcL

                  hemoglobin greater than or equal to 10mg/dL

                  total bilirubin less than or equal to 1.5 X institutional upper limit of normal

                  AST(SGOT)/ALT(SGPT) less than or equal to 3 X institutional upper limit of normal

                  creatinine less than or equal to 1.5 X institutional upper limit of normal

                  OR

                  measured creatinine clearance greater than or equal to 45 mL/min/1.73 m2 for
                  participants with

                  creatinine levels above institutional normal.

              16. Potassium (K) should be within the range of greater than or equal to 3.6 mEq/L.

              17. Women of childbearing potential must have a negative urine or serum pregnancy
                  test within 7 days prior to the start of the study.

              18. The effects of LY2606368 on the developing human fetus are unknown. For this
                  reason, all subjects of reproductive potential must agree to use adequate
                  contraception prior to study entry, for the duration of study participation, and
                  for at least four months following the last dose of experimental therapy. All
                  subjects of reproductive potential must also agree to use both a barrier method
                  and a second method of birth control during the course of the study and for four
                  months after the last dose of study drug(s). Should a woman become pregnant or
                  suspect she is pregnant while she is participating in this study, she should
                  inform her treating physician immediately.

              19. Ability of subject to understand, adhere to protocol requirements and the
                  willingness to sign a written informed consent document.

        EXCLUSION CRITERIA:

          1. Participants who are receiving any other investigational agents.

          2. Participants with known brain metastases should be excluded from this clinical trial
             because of their poor prognosis and because they often develop progressive neurologic
             dysfunction that would confound the evaluation of neurologic and other adverse events.
             Participants with brain metastases diagnosed greater than 1 year prior to study entry
             may be considered if they received sterilizing therapy to the CNS (resection or
             radiation) and have been CNS recurrence-free for the 1-year period.

          3. Participants who have had prior treatment with LY2606368 or other Chk inhibitors

          4. Participants with a serious cardiac condition, such as congestive heart failure; New
             York Heart Association Class III/IV heart disease; unstable angina pectoris;
             myocardial infarction within the last 3 months; valvulopathy that is severe, moderate,
             or deemed clinically significant despite medical intervention; or arrhythmias that are
             symptomatic or refractory to medical intervention.

          5. Participants who have QTc interval of > 470 msec on a screening electrocardiogram.

          6. Participants with a prior history of drug-induced serotonin syndrome, or a family
             history of long-QT syndrome.

          7. Lack of recovery of prior adverse events due to prior cancer therapy to Grade less
             than or equal to 1 (NCI CTCAE; except alopecia). Electrolyte abnormalities that are
             corrected with supplementation will be eligible. Participants with platinum-related
             grade 2 or greater hypomagnesemia (on replacement) will be eligible. Stable persistent
             grade 2 peripheral neuropathy may be allowed as determined on a case-by-case basis at
             the discretion of the PI.

          8. Uncontrolled intercurrent illness including, but not limited to, symptomatic
             congestive heart failure, unstable angina pectoris, cardiac arrhythmia, clinically
             significant GI bleeding or hemoptysis within 28 days prior to the start of the study,
             or psychiatric illness/social situations that would limit compliance with study
             requirements.

          9. Participants with active infection will not be eligible, but may become eligible once
             infection has resolved and they are at least 7 days from completion of antibiotics.

         10. Another previous or current invasive malignancy within the last 2 years, with the
             exception of curatively treated stage Ia cervical carcinoma, or resected stage Ia
             endometrial cancer, and noninvasive nonmelanoma skin cancers. Participants with
             gBRCA1/2m and primary breast or ovarian cancers will be eligible for Cohort 1.

         11. HIV-positive participants on combination antiretroviral therapy are ineligible because
             of the potential for pharmacokinetic interactions with LY2606368. HIV- positive
             participants who are not on HAART and have CD4 counts > 500 will be considered on an
             individual basis.