AZD6738 First Time in Patient Multiple Ascending Dose Study

Inclusion Criteria: 1. Provision of signed and dated, written informed consent prior to any study specific procedures, sampling and analyses. 2. For the dose escalation phase, Part A, histological or cytological confirmation of relapsed or refractory B cell malignancy, including CLL, PLL, Burkitt lymphoma/Burkitt cell leukaemia, acute lymphocytic leukaemia, hairy cell leukaemia (HCL) and aggressive and indolent B cell lymphoma, not considered to be appropriate for further conventional treatment. For the dose expansion phase, Part B, histological or cytological confirmation of relapsed or refractory 11q-deleted or ATM-deficient CLL, not considered to be appropriate for further conventional treatment. 3. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 with no deterioration over the previous 2 weeks and an estimated life expectancy of greater than 16 weeks. 4. Not known to be positive for HIV antibody, Hepatitis B surface antigen and Hepatitis C antibody. 5. Females must be using adequate contraceptive measures, must not be breast feeding and must have a negative pregnancy test prior to start of dosing if of child-bearing potential or must have evidence of non-child-bearing potential by fulfilling one of the following criteria at screening: * Post menopausal defined as aged more than 50 years and amenorrhoeic for at least 12 months following cessation of all exogenous hormonal treatments. * Documentation of irreversible surgical sterilisation by hysterectomy, bilateral oophorectomy or bilateral salpingectomy but not tubal ligation. * Amenorrhoeic for 12 months and serum follicle-stimulating hormone (FSH), luteinizing hormone (LH) and plasma oestradiol levels in the postmenopausal range for the institution. 6. Ability to swallow and retain oral medication Exclusion Criteria: 1. Receiving, or having received during the four weeks prior to study entry (signing of consent), treatment for their malignancy. 2. Receiving, or having received during the four weeks prior to study entry (signing of consent), corticosteroids (at a dose \> 10 mg prednisone/day or equivalent) for any reason. 3. A known hypersensitivity to AZD6738 or any excipient of the product. 4. Treatment with any investigational medicinal product (IMP) within 28 days prior to signing of consent. 5. Receiving, or having received, concomitant medications, herbal supplements and/or foods that significantly modulate CYP3A4 or Pgp activity (wash out periods of two weeks, but three weeks for St. John's Wort). Note these include common azole antifungals, macrolide antibiotics. 6. Impaired hepatic or renal function as demonstrated by any of the following laboratory values: 1. Albumin \< 33g/L 2. AST or ALT \> 2.5 x ULN 3. Total bilirubin \> 1.5 x ULN 4. Alkaline phosphatase \> 2.5 x ULN 5. Glomerular filtration rate (GFR) \< 50 mL/min, as assessed using the standard methodology at the investigating centre (i.e. Cockroft-Gault, MDRD or CKD-EPI formulae, EDTA clearance or 24 h urine collection) 6. Serum creatinine \> 1.5 x ULN 7. Haematuria: +++ on microscopy or dipstick 8. AST, ALT, ALP, bilirubin or renal function that, in the opinion of the investigator, is unstable or worsening 7. INR \> 1.5 or other evidence of impaired hepatic synthesis function Persisting (\> 8 weeks) severe pancytopenia due to previous therapy rather than disease (ANC \< 0.5 x 109/L or platelets \< 50 x 109/L) - to be confirmed via bone marrow biopsy, as part of normal clinical care, prior to signing of consent 8. CNS involvement with malignancy 9. Cardiac dysfunction as defined as: Myocardial infarction within six months of study entry, NYHA Class II/III/IV heart failure, unstable angina, unstable cardiac arrhythmias or reduced LVEF \< 55% 10. Any of the following cardiac criteria: 1. Mean resting corrected QT interval (QTc) \>470 msec obtained from 3 electrocardiograms (ECGs) in 24 hours 2. Any clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g., complete left bundle branch block, third degree heart block) 3. Any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as heart failure, hypokalaemia, congenital long QT syndrome, immediate family history of long QT syndrome or unexplained sudden death under 40 years of age 11. Patients at risk of brain perfusion problems, e.g., carotid stenosis 12. Patients with relative hypotension (\< 100/60 mm Hg) or clinically relevant orthostatic hypotension, including a fall in blood pressure of \>20mm Hg 13. Uncontrolled hypertension requiring clinical intervention 14. Any other malignancy which has been active or treated within the past three years, with the exception of cervical intra-epithelial neoplasia and non-melanoma skin cancer 15. Refractory nausea and vomiting, chronic gastrointestinal diseases or previous significant bowel resection that would preclude adequate absorption of AZD6738 16. Patients with uncontrolled seizures 17. Active infection requiring systemic antibiotics, antifungal or antiviral drugs 18. Concurrent severe and/or uncontrolled medical condition (e.g., severe COPD, severe Parkinson's disease, active inflammatory bowel disease) or psychiatric condition