A research study looking at a new treatment for patients with advanced cancer, to investigate different doses of the experimental study drug, EP0042, in order to determine a dose, which is safe, well tolerated and likely to be effective in treating AML (acute myeloid leukaemia).

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• Core Exclusion Criteria: 1. Suspected brain and/or leptomeningeal metastases that are symptomatic or untreated or that require current therapy. 2. Ongoing toxic manifestations of previous treatments that have not reduced to at least Common Terminology Criteria for Adverse Events (CTCAE) Grade 1. Exceptions to this are alopecia or certain Grade 2 treatment related toxicities, which in the opinion of the Investigator should not exclude the patient. 3. Creatinine clearance (calculated using Cockcroft-Gault formula, or measured) < 50 mL/min. 4. Receiving an investigational anti-cancer treatment concurrently or within 14 days or five half-lives of either the parent drug or any active metabolite prior to the start of treatment with EP0042. Patients with AML may receive hydroxyurea throughout the screening period and during the first 2 cycles of study treatment in the first module(FIH study). 5. Current refractory nausea and vomiting, malabsorption syndrome, disease significantly affecting gastrointestinal(GI) function, resection of the stomach, extensive small bowel resection that is likely to affect absorption, symptomatic inflammatory bowel disease, partial or complete bowel obstruction, or gastric restrictions and bariatric surgery such as gastric bypass. 6. Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection per institutional protocol. Testing for HBV or HCV status is not necessary unless clinically indicated or the patient has a history of HBV or HCV infection. 7. Patients with active human immunodeficiency virus infection (HIV) infection (testing is not required). Patients living with HIV will be eligible if they have CD4+ T-cell count ≥ 350 cells/μL, no history of AIDS-defining opportunistic infections in the past 12 months, and can be managed on a regimen consistent with this protocol's permitted concomitant medications. 8. Malignant disease other than that being treated in this study, with the following exceptions: a. Malignancies that were treated curatively and have not recurred within 2 years prior to study treatment. b. Completely resected basal cell and squamous cell skin cancers. c. Any malignancy considered to be indolent and that has never required therapy. d. Completely resected carcinoma in situ of any type. 9. Any medical condition that would, in the investigator's judgment, prevent the patient's participation in the clinical study due to safety concerns, compliance with clinical study procedures, or interpretation of study results. 10. Any major surgical procedure (in the investigator's judgement) within 2 weeks of the first dose of study drug. 11. Pregnant, likely to become pregnant, or lactating women (where pregnancy is defined as the state of a female after conception and until the termination of gestation).