Additional Study Information: This study is a Phase 1 clinical trial, which means it is the first stage of testing a new drug in humans to evaluate its safety, determine how the body processes it, and identify any potential side effects. The drug being studied, DZD6008, is investigational, meaning it has not been approved by the U.S. Food and Drug Administration (FDA). This study is evaluating the study drug, DZD6008, in patients with advanced non small cell lung cancer (NSCLC) harboring an epidermal growth factor receptor (EGFR) mutation. EGFR is a protein that is important in regulating activities in cell proliferation. The main purpose of the study is to learn if the study drug is safe and tolerable (if it will cause harmful effects), and effectiveness in patients diagnosed with advanced NSCLC with positive EGFR gene mutations. The study will also measure concentration levels of study drug, DZD6008, in plasma, and explore how the human body takes up, breaks down, and clears the study drug (and metabolites if applicable), a field of study that is known as pharmacokinetics (PK). Additional analyses may be conducted with PK blood samples to further study possible drug metabolites or validate the analytical method.