Inclusion Criteria:  Participants must have a histologically confirmed advanced pancreatic adenocarcinoma that is not curable with standard approaches based on the judgement of the treating investigator. Patients with metastatic pancreatic cancer and unresectable pancreatic cancer are eligible. Patients must have progressed on a platinum-based regimen prior to enrolling on the trial. Patients must have received no more than 1 prior lines of platinum-based chemotherapy in the metastatic setting. Therapy given in the adjuvant or neoadjuvant setting is counted as a prior therapy if it occurred less than 6 months before cancer recurrence or progression. Age ≥ 18 years. As no dosing or adverse event data are currently available in participants < 18 years of age, children and adolescents are excluded from this study. ECOG performance status of 0 or 1 (see Appendix A).  Participants must have adequate organ and marrow function as defined below:  Absolute neutrophil count ≥ 1,500/mm3 Platelets ≥ 100,000/mm3 Hemoglobin ≥ 9 g/dL Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN); or total bilirubin ≤3.0 x ULN with direct bilirubin WNL in patients with documented Gilbert's Syndrome. Alanine aminotransferase (ALT) and ≤ 3 × institutional ULN; or ≤ 5 × institutional aspartate aminotransferase (AST) ULN if known hepatic metastases Albumin ≥ 2.7 g/dL Serum creatinine ≤ 1.5 × institutional ULN -OR- Creatinine clearance measured creatinine clearance (CrCl) ≥50 mL/min as calculated by either the Cockcroft-Gault method, a 24-hour urine test or another validated test as per local practice (confirmation of creatinine clearance is only required when creatinine is >1.5 x institutional ULN)  Cockcroft-Gault equation for estimated CrCL:  CrCl (glomerular filtration rate [GFR]) = (140-age) x (weight/kg) x Fa (72 x serum creatinine mg/dL)  where F= 0.85 for females and F=1 for males - Participants must have measurable disease by RECIST v. 1.1 criteria and be willing to undergo a pre-treatment and on-treatment tumor biopsy. The biopsy requirement can be waived only with approval from the sponsor-investigator.  For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Patient has read and understands the informed consent form (ICF) and has been given written ICF prior to any study procedures which includes compliance with the requirements and restrictions listed in the ICF and in this protocol.  Female patients who are not of child-bearing potential* and women of childbearing potential who agree to use adequate contraceptive measures from 2 weeks prior to the study and 5x half-lives of adavosertib + 6 months after study treatment discontinuation, who are not breastfeeding, and who have a negative serum or urine pregnancy test within 7 days prior to the start of study treatment.  * Evidence of non-childbearing status, defined as below:  -- Women who are surgically sterile (i.e., have undergone bilateral salpingectomy, bilateral oophorectomy, or complete hysterectomy).  -- Age ≥50 years with any one or more of the conditions below:  Amenorrheic for 12 months or more following cessation of all hormonal replacement therapy Had radiation-induced menopause with last menses >1 year ago Had chemotherapy-induced menopause with last menses >1 year ago Age <50 if amenorrhoeic for 12 months or more following cessation of all hormonal replacement therapy and if luteinizing hormone and follicle-stimulating hormone levels are in the post-menopausal range per institutional standards of practice. Male patients should be willing to abstain or use barrier contraception (i.e., condoms) for the duration of the study drug exposure and for 5x half-lives of adavosertib + 3 months after study treatment discontinuation. Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.  Exclusion Criteria:  - Patients who have previously received adavosertib are not eligible.  - Use of an anti-cancer treatment drug ≤ 21 days or 5 half-lives (whichever is shorter) prior to the first dose of adavosertib (AZD1775).  - Any prior palliative radiation must have been completed at least 7 days prior to the first dose of adavosertib, and patient must have recovered from any acute adverse effects, that the treating investigator thinks could impair the tolerance of the study drugs, prior to the start of study treatment.  - Participants who have undergone major surgical procedures ≤ 28 days, or minor surgical procedures ≤ 7 days, of the first dose of adavosertib. No waiting period is required following port-a-cath or other central venous access placement.  - Presence of CTCAE v5.0 Grade >1 toxicity from prior therapy (except alopecia, anorexia or CTCAE grade 2 peripheral neuropathy).  - Patient is unable to swallow oral medications. Note: Patient may not have a percutaneous endoscopic gastrostomy (PEG) tube or be receiving total parenteral nutrition (TPN).  - Participants with known malignant central nervous system (CNS) disease other than neurologically stable, treated brain metastases - defined as metastasis having no evidence of progression or hemorrhage for at least 2 weeks after the completion of treatment (including brain radiotherapy). Must be off any systemic corticosteroids for the treatment of brain metastases for at least 14 days prior to enrollment.  - Participants receiving any medications or substances that are known to be moderate to strong inhibitors or inducers of CYP3A4 and which cannot be discontinued at least 2 weeks prior to the first dose of adavosertib 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. Refer to Protocol Section 5 for information on prohibited concomitant medications.  - Use of herbal medications or supplements within 7 days prior to the first dose of adavosertib.  - History of hypersensitivity to compounds of similar chemical or biologic composition to gemcitabine or adavosertib.  - Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or psychiatric illness/social situations that would limit compliance with study requirements.  - Known HIV-positive participants are ineligible because these participants are at increased risk of lethal infections when treated with marrow-suppressive therapy.  - Participants with a clinically significant gastrointestinal disorder that in the opinion of the treating investigator could impact the absorption of the study drugs, including but not limited to refractory nausea and vomiting, chronic gastrointestinal disease, inability to swallow the formulated product, or previous significant bowel resection that would preclude adequate absorption, distribution, metabolism, or excretion of adavosertib.  - Participants with a history of a clinically relevant second primary malignancy within the past 2 years. Exceptions include: resected basal and squamous cell carcinomas of the skin and completely resected carcinoma in situ of any type.  - Pregnant or lactating women are excluded from this study because gemcitabine/adavosertib are anti-cancer agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with gemcitabine/adavosertib, breastfeeding should be discontinued if the mother is treated with gemcitabine/adavosertib.  Any of the following cardiac diseases currently or within 6 months of the first dose of adavosertib:  -- Unstable angina pectoris  -- Acute myocardial infarction  -- Congestive heart failure ≥ Class 2 (as defined by New York Heart Association (NYHA))  -- Conduction abnormality not controlled with pacemaker or medication  Significant ventricular or supraventricular arrhythmias (patients with chronic rate-controlled atrial fibrillation in the absence of other cardiac abnormalities are eligible) History of Torsades de pointes unless all risk factors that contributed to Torsades have been corrected.  Participants ECG must not meet the following criteria:  Resting corrected QTc interval using the Fridericia formula (QTcF) >480 msec (as calculated per institutional standards) (Note: if one ECG performed as screening demonstrates a QTcF > 480 msec, then a mean QTcF of ≤ 480 msec obtained from 3 ECGs 2-5 minutes apart, is required at study entry for the participant to be considered eligible) congenital long QT syndrome