Evaluate Safety, Tolerability, Pharmacokinetics and Anti-tumor Activity of AZD3759

Inclusion criteria: 1. Subjects must provide written informed consent before any study related procedure. 2. Male or female Chinese patients ≥18 years old. 3. Histologically or cytologically confirmed non-small cell lung cancer with activating mutation in EGFR gene (including Exon19Del and/or L858R). A validated and robust test method reviewed and approved by the regulatory authority should be used to determine EGFR mutation status in tissue or plasma locally. 4. Patients with advanced non-small cell lung cancer (stage IV) with documented BM and/or LM. Part A dose escalation can include EGFR TKI-naïve NSCLC patients with measurable lung lesion and no BM. Patients with BM and/or LM in each dose group shall account for at least one-third. 5. According to Eastern Cooperative Oncology Group (ECOG) Scale, performance status is grade 0 to 1, without worsening in the past 2 weeks, and life expectancy of at least 3 months. If ECOG performance status is grade 2 due to LM disease, the patient can also be enrolled. 6. Non-surgical sterilized women of child-bearing potential and male subjects shall agree to take medically acceptable contraception measures during dosing of investigational drug and 3 months after completion of study treatment. Non-surgical sterilized women of child-bearing potential must have negative blood pregnancy test at screening. 7. Asymptomatic BM patients who have not received prior treatment with any EGFR TKI or symptomatic BM patients who are not warranted temporally for definitive local treatment (surgery or radiotherapy). For patients with prior local treatment for BM lesion (surgery or radiotherapy), intracranial lesion progression is required. 8. BM patients must have at least one measurable intracranial lesion; in case of prior radiotherapy for BM lesion, progression is required and must meet measurable lesion criteria again. Measurable extracranial disease is not required. 9. LM patients must be confirmed by the presence of malignant cells by cerebrospinal fluid (CSF) cytology. Diagnosis of LM disease by MRI alone does not meet inclusion criteria. Patients with both BM and LM are considered as LM. 10. LM patients must have at least one leptomeningeal lesion which shows visible abnormality by MRI. Measurable extracranial disease is not required. Exclusion criteria: Patients meeting any of the following criteria cannot participate in the study: 1. Have taken any other investigational drug in a clinical trial within 30 days prior to initial dose. 2. Prior treatment with any EGFR TKI within 8 days or 5 half-lives of the drug (see table 19 Washout of EGFR TKIs) prior to initial dose of study drug. If the washout period for the EGFR TKI cannot be reached due to schedule or pharmacokinetic properties, an alternative washout period can be proposed based on recovery period of known adverse drug reactions, which must be agreed to in advance by the Investigator and the Sponsor. 3. T790M mutation positive patients. 4. Have received previous treatment regimen including any cytotoxic chemotherapy or other anti-cancer drugs (other than EGFR TKIs) for treatment of advanced non-small cell lung cancer within 14 days prior to initial dose of study drug. 5. Patients with medically uncontrollable seizures and/or untreated (eg., requiring mannitol and/or placement a VP shunt) intracranial hypertension are excluded. 6. Have undergone major surgical procedure (excluding placement of vascular indwelling needle) or serious trauma within 4 weeks prior to initial dose of study drug, or major surgical procedure is expected during the study. 7. Patients who have received radiotherapy for a large area within 4 weeks, or local palliative radiotherapy for a small area within 1 week prior to initial dose of study drug (for subjects requiring radiotherapy for more than 30% bone marrow, the radiotherapy must be completed before 4 weeks prior to initial dose). 8. BM and LM patients who have received whole-brain radiotherapy. 9. Patients with a history of allergy to AZD3759 and its structural analogues (Gefitinib) or pharmaceutical excipients (whether active or not). 10. Subjects who are receiving (or cannot discontinue at least 1 week prior to initial dose of study drug) any drug or traditional Chinese medicine known to inhibit or induce CYP3A4 or CYP3A5 activity.