AZD3470 as Monotherapy or in Combination With Anticancer Agent(s) in Participants With Haematologic Malignancies.

Inclusion Criteria: Core Inclusion criteria: 1. Adequate adult (ECOG) or adolescent (Karnofsy or Lanksy) Performance Score assessments 2. Adequate organ and bone marrow function. Module 1 Cohort 1: 1. Age: 1. Part A (dose escalation): aged ≥ 18 years at the time of signing the informed consent. 2. Part B (optimization): aged ≥ 12 years of age. Adolescent participants must weigh ≥ 40 kg. 2. Histologically confirmed diagnosis of cHL based on WHO criteria 3. Previous treatment with at least 2 prior lines of therapy for the treatment of cHL (including at least 2 cycles of BV and anti-PD1) and have documented r/r active disease requiring treatment. 4. Participants must provide FFPE baseline tumour tissue. 5. At least 1 radiographically measurable, and/or FDG-avid lymphoma lesion ( \>1.5 cm for nodal lesion and \>1 cm for extranodal lesion). Module 1 Cohort 2: 1- Participants must be at least 50 years of age or older at study entry. 2- Histologically confirmed diagnosis of cHL based on WHO criteria 3- Ann Arbor stages III or IV. 4- Participant must have previously received at least 4 cycles of SoC combination therapy with A-AVD, N-AVD, AVD, or ABVD (based on regional SOC, per investigator) as finite first-line induction therapy, and achieved at least a PR post-induction therapy. 5- Participants must provide FFPE baseline tumour tissue. Module 1 Cohort 3: 1. Participants must be aged ≥ 18 years at the time of signing the informed consent. 2. Histologically confirmed diagnosis of PTCL NOS, systemic ALCL, or AITL based on WHO criteria. 2a- If pre-screening for MTAP deficiency is initiated, all participants must be MTAP deficient as determined by a local test. 3- Participants must have received at least 1 prior line of therapy for the treatment of PTCL and have exhausted all available therapies with demonstrated clinical benefit. Participants with ALCL must have received prior BV treatment. 4- Participants must provide FFPE baseline tumour tissue 1. Ability to provide an on-treatment biopsy (if the tumour is suitable for biopsy). 5- At least 1 radiographically measurable, and/or FDG-avid lymphoma lesions (\> 1.5 cm for nodal lesion and \>1 cm for extranodal lesion). Module 2 Cohort 1: 1- Participants must be aged ≥ 18 years at the time of signing the informed consent. 2- Histologically confirmed diagnosis of cHL based on WHO criteria 3- At least 1 radiographically measurable, and/or FDG-avid lymphoma lesions (\> 1.5 cm for nodal lesion and \>1 cm for extranodal lesion). 4- Participant must have received at least 1 prior line of therapy for the treatment of cHL and have documented r/r active disease requiring treatment. 5- Participants must provide FFPE baseline tumour tissue. Exclusion Criteria: Core Exclusion criteria: 1. Any significant laboratory finding or any severe and uncontrolled medical condition. 2. Active CNS involvement by lymphoma, leptomeningeal disease, or spinal cord compression. 3. Serologic active HBV or HCV infection. 4. Known to have tested positive for HIV. 5. Active gastrointestinal disease or other condition that will interfere with oral therapy. 6. Any of the following ECG cardiac criteria: Mean resting QTcF \> 470 msec, clinically important abnormalities in rhythm, conduction or morphology, and/or any factors that increase the risk of QTc prolongation or risk of arrhythmic events. 7. Undergone any of the following procedures within 6 months prior to first dose: a) Coronary artery bypass graft, b) Percutaneous coronary intervention or heart valve replacement or repairment, c) Vascular stent implantation (venous stent is eligible), d) Acute coronary syndrome / myocardial infarction, e) Unstable or poorly controlled angina pectoris, f) Ventricular arrhythmias requiring continuous therapy, g) Uncontrolled atrial fibrillation, h) Haemorrhagic or thrombotic stroke (including transient ischaemic attacks) or any other CNS bleeding. i) Acute venous or atrial thromboembolic event (unless considered stable or adequately treated with at least 3months of therapeutic anticoagulation). 8. Severe valvular heart disease. 9. Congestive heart failure Grade II to Grade IV. 10. Prior or current cardiomyopathy. 11. Uncontrolled hypertension. 12. History of significant haemoptysis or haemorrhage within4 weeks of the first dose of study treatment. 13. Unresolved toxicities of Grade \> 1 from prior anti cancer therapy (excluding peripheral neuropathy, vitiligo, alopecia and endocrine disorders that are controlled with replacement hormone therapy, and asymptomatic laboratory abnormalities), unless immune-mediated. 14. History of another primary malignancy. 15. Received the following anticancer therapies: anti-lymphoma therapy (within 21 days), radiation therapy(within 28 days), allo-HSCT (within 180 days), auto-HSCT/cellular therapy (within 60 days), or MAT2A or PRMT5 inhibitor 16. Requires ongoing immunosuppressive therapy, including systemic corticosteroids. 17. Psychiatric illness/social situations/substance abuse disorders that would limit compliance with study requirements or compromise the ability to give written informed consent. 18. Use of prescription medications that are known as: 1. Strong or moderate inhibitors or inducers of CYP3A4, sensitive substrates of CYP3A4, inhibitors or substrates of CYP2D6, inhibitors and sensitive substrates of CYP2C8, and NTI substrates of CYP3A4, CYP2D6, and CYP2C8. 19. Received live, attenuated vaccine within 30 days prior to first dose of treatment. 20. Known hypersensitivity to AZD3470 or any of the excipients of the product. 21. Involvement in planning or conduct of the study (applies to both AstraZeneca staff and site staff). 22. Judgement by investigator that the participant is unlikely to comply with study procedures, restrictions, and requirements. 23. Previous enrolment in the present study. 24. Pregna