The study will be conducted in two segments. The first segment of the study (Phase 1a) will be a dose escalation design in order to determine the Maximum Tolerated Dose (MTD) of AZD4635 given as monotherapy and in combination with durvalumab. The MTD will be determined by assessing adverse events and the incidence of abnormal laboratory measures. Once the maximum tolerated monotherapy dose of AZD4635 has been determined, combination dosing with durvalumab will start in a new cohort of patients at one dose level lower than the highest tolerated dose of AZD4635 monotherapy. The combination therapy cohorts in Phase 1a will also have a 2-week monotherapy lead-in after which patients who tolerate monotherapy AZD4635 will then continue twice daily dosing of AZD4635 in combination with durvalumab (anti programmed-death ligand 1 [PD-L1]) at the fixed dose of 1.5 grams IV every 4 weeks.