Inclusion Criteria:  Histologically or cytologically documented, locally advanced or metastatic solid tumour, excluding lymphoma, for which standard therapy does not exist or has proven ineffective or intolerable. Eastern Cooperative Oncology Group performance status score of 0 or 1. Predicted life expectancy ≥ 12 weeks. Patients must have normal organ and marrow function at baseline, within 7 days prior to study drug administration. Males and females of childbearing potential who agree to use contraceptive measures must be consistent with clinical study protocol.  Exclusion Criteria:  Persistent toxicities (Common Terminology Criteria for Adverse Events [CTCAE] Grade > 2) caused by previous anticancer therapy, excluding alopecia and CTCAE Grade 2 peripheral neuropathy. 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, itraconazole, rifampicin, and omeprazole. Any significant cardiac diseases currently or within the last 6 months such as: (a) unstable angina pectoris (b) acute myocardial infarction, congestive heart failure (c) conduction abnormality not controlled with pacemaker or medication (d) significant ventricular or supraventricular arrhythmias.  Any of the following:  History or current evidence of congenital long QT syndrome; concomitant medications known to prolong QT interval or history of medicationrelated QT prolongation. Known to have tested positive for human immunodeficiency virus or active tuberculosis infection. Known active hepatitis infection, positive hepatitis C antibody, hepatitis B virus surface antigen or hepatitis B virus core antibody, at screening. Any evidence of diseases (such as severe or uncontrolled systemic diseases, including uncontrolled hypertension, renal transplant, active infections, and active bleeding diseases) which prohibit participating in the study. Spinal cord compression or brain metastases unless asymptomatic, stable, and not requiring steroids for at least 4 weeks prior to start of study intervention. Receipt of live virus and live bacterial vaccines whilst the patient is receiving the study intervention and during the 30-day follow-up period. Inactivated flu vaccines are permitted. Use of an anti-cancer treatment drug ≤ 21 days (≤ 6 weeks for nitroureas or mitomycin C) or use of an investigational product within 5 half-lives prior to the first dose of adavosertib. Patient uses drugs that are sensitive to CYP3A4 substrates or CYP3A4 substrates with a narrow therapeutic index, or are moderate to strong inhibitors/inducers of CYP3A4 which cannot be discontinued 2 weeks or 5 halflives (whichever is longer) prior to Day 1 of dosing. Patients with a known hypersensitivity to adavosertib, itraconazole, rifampicin, and omeprazole or any of the excipients of the product. Currently pregnant (confirmed with positive pregnancy test) or breast-feeding.