This study will treat patients with advanced NSCLC who have progressed following prior therapy. This is the first time this drug has ever been tested in patients, and so it will help to understand what type of side effects may occur with the drug treatment. It will also measure the levels of drug in the body and preliminarily assess its anti-cancer activity as monotherapy and in combination with Osimertinib.

A phase I/II, open-label, multicentre study to investigate the safety, tolerability, pharmacokinetics and anti-tumour activity of AZD4205 as monotherapy or in combination with Osimertinib in patients with EGFR mutant advanced stage non-small cell lung cancer (NSCLC). This study includes dose escalation part and dose expansion part.

Inclusion Criteria:

1. Obtained written informed consent
2. Patients must have histological or cytological confirmation of activating EGFR mutation positive NSCLC and have failed prior EGFR TKIs treatment.
3. Patients must exhibit Eastern Cooperative Oncology Group (ECOG) performance status 0-1
4. Adequate bone marrow reserve and organ system functions

Exclusion Criteria:

1. Any unsolved toxicity > CTCAE grade 1 from previous anti-cancer therapy (except alopecia)
2. Active viral or bacterial infections;
3. Active or latent tuberculosis;
4. History of interstitial lung disease (ILD)
5. History of heart failure or QT interval prolongation
6. Immunodeficiency diseases;
7. Active CNS metastases
8. Treatment with an EGFR TKI (e.g., erlotinib or gefitinib) within 8 days or approximately 5 x half-life, whichever is longer, of the first dose of study treatment