-  ELIGIBILITY CRITERIA:

          -  Patients must have histologically confirmed solid tumors for which all standard
             therapy known to prolong survival have failed or for which standard therapies do not
             exist.

          -  Patients must have measurable disease or evaluable disease for the escalation phase;
             for the 6 additional patients enrolled at maximum tolerated dose (MTD) for further
             evaluation of pharmacokinetics (PK) and pharmacodynamics (PD) endpoints (Expansion
             Cohort A). For the 6-patient breast cancer gene (BRCA)-mutation expansion cohort,
             patients must have measurable disease; however, tumor biopsies are optional. For
             Expansion Cohort B, patients must have tumor amenable to biopsy (excisional or
             incision biopsies of skin or head (H) & neck (N) lesions under visualization) and
             willingness to undergo a tumor biopsy or patient will be undergoing a procedure due to
             medical necessity during which the tissue may be collected, or tumor biopsy tissue
             from a previous research study or medical care is available for submission at
             registration. Criteria for the submission of tissue are:

               -  Tissue must have been collected within 3 months prior to registration

               -  Patient has not received any intervening therapy for their cancer since the
                  collection of the tumor sample

               -  Tumor tissue must meet the minimum requirements

          -  Patients must have completed any chemotherapy, radiation therapy, surgery, or biologic
             therapy greater than or equal to 3 weeks (or > 5 half-lives, whichever is shorter)
             prior to entering the study. Patients must be greater than or equal to 2 weeks since
             any prior administration of a study drug in an exploratory Investigational New Drug
             (IND)/Phase 0 study or more than or equal to 1 week from palliative radiation therapy.
             Patients must have recovered to eligibility levels from prior toxicity or adverse
             events.

          -  Age greater than or equal to 18 years of age.

          -  Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 1
             (Karnofsky >60%)

          -  Life expectancy of greater than 3 months.

          -  Patients must have normal organ and marrow function 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 >9 g/dL

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

               -  Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase
                  (SGOT)/alanine aminotransferase (ALT) serum glutamate-pyruvate transaminase
                  (SGPT) less than or equal to 3 times institutional upper limit of normal

               -  creatinine less than or equal to 1.5 times institutional upper limit of normal OR

               -  creatinine clearance greater than or equal to 60 mL/min/1.73 m(2) for patients
                  with creatinine levels above institutional normal.

          -  The effects of Adavosertib (AZD1775) on the developing human fetus are unknown. For
             this reason and because molecular inhibitors of Wee1 kinase are known to be
             teratogenic, women of child-bearing potential (WoCBP) may be included only if
             acceptable contraception is in place for two weeks before study entry, for the
             duration of the treatment with the study drug, and for 2 months after the last dose of
             AZD1775. Male patients who are involved in the study must agree to avoid procreative
             and unprotected sex (i.e., by using acceptable forms of contraception) and must not
             donate sperm during the study and for 3 months after the last dose of AZD1775. Where
             the female partner is pregnant or not using effective birth control, men should be
             advised to abstain while in the study and for 3 months after the last dose of AZD1775.
             Female partners, who are of child-bearing potential, of men participating in clinical
             studies of AZD1775 will also be required to use effective contraceptive measures while
             their partner is on study drug and for 3 months thereafter. Male patients will be
             advised to arrange for the freezing of sperm samples prior to the start of the study
             should they wish to father children while on AZD1775 or during the 3 months after
             stopping AZD1775.

          -  Because there is an unknown but potential risk for adverse events in nursing infants
             secondary to treatment of the mother with the study drugs, breastfeeding should be
             discontinued prior to the first of study drug and women should refrain from nursing
             throughout the treatment period and for 14 days following the last dose of study drug.

          -  Patients must be able to swallow whole tablets or capsules. Nasogastric or G-tube
             administration is not allowed. Any gastrointestinal disease which would impair ability
             to swallow, retain, or absorb drug is not allowed.

          -  Ability to understand and the willingness to sign a written informed consent document.

          -  Patients with prostate cancer can continue to receive treatment with
             gonadotropin-releasing hormone (GnRH) agonists while on study, as long as there is
             evidence of disease progression on therapy.

        EXCLUSION CRITERIA:

          -  Patients who are receiving any other investigational agents.

          -  Patients with known active brain metastases or carcinomatous meningitis are excluded
             from this clinical trial. Patients whose brain metastatic disease status has remained
             stable for greater than or equal to 4 weeks following treatment of brain metastases
             are eligible to participate at the discretion of the principal investigator.

          -  Eligibility of subjects receiving any medications or substances with the potential to
             affect the activity or pharmacokinetics of AZD1775 will be determined following review
             by the principal investigator.

          -  Patients receiving any medications or substances that are inhibitors or inducers of
             Cytochrome P450 3A4 (CYP3A4), or CYP3A4 substrates need to be reviewed by the
             principal investigator. Continuation of such medications will be at the discretion of
             the principal investigator. Concomitant use of aprepitant or fosaprepitant is
             prohibited. As grapefruit and Seville oranges are known to contain moderate inhibitors
             of CYP3A4, these fruits or their products (including marmalade, juice, etc.) should be
             avoided while taking AZD1775. The use of sensitive substrates of CYP3A4, such as
             atorvastatin, simvastatin and lovastatin, is also prohibited in this study. Herbal
             preparations are not allowed throughout the study. These herbal medications include
             but are not limited to: St. John's wort, kava, ephedra (mahung), gingko biloba,
             dehydroepiandrosterone (DHEA), yohimbe, saw palmetto and ginseng.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements.

          -  Pregnant women are excluded from this study because the effects of the study drugs on
             the developing fetus are unknown.

          -  Human immunodeficiency virus (HIV) positive patients on antiretroviral therapy are
             ineligible because of the potential for pharmacokinetics (PK) interactions.

        INCLUSION OF WOMEN AND MINORITIES:

        Both men and women of all races and ethnic groups are eligible for this trial.