The goal of this clinical trial is to assess the safety and tolerability of QLS1209 alone in patients with eligible advanced solid tumors，determine the maximum tolerated dose (MTD) or maximum drug dose（MAD）of QLS1209, identify a recommended phase 2 dose (RP2D) and preferred schedule, examine preliminary pharmacokinetics (PK) and assess anti-tumor activity.

Inclusion Criteria:

• Volunteer to participate in this clinical study; completely understand and know this study as well as sign the informed consent form (ICF);
• Age ≥ 18 years when ICF is signed;
• Eastern Cooperative Oncology Group performance status of 0 or 1;
• Expected survival ≥ 3 months;
• advanced malignant solid tumors who have failed standard treatment or have received no standard treatment；
• a) CCNE1 amplification determined by tumor or plasma next generation sequencing (NGS) or fluorescence in-situ hybridization (FISH); b) FBXW7 mutation determined by tumor or plasma NGS; c) PPP2R1A mutation determined by tumor or plasma NGS;
• Subjects with at least one evaluable tumor lesion (dose-escalation stage) or at least one measurable tumor lesion (dose-expansion stage) according to RECIST v1.1;

Exclusion Criteria:

• Previous treatment with PKMYT1 inhibitors;

• Received chemotherapy, biological therapy, endocrine therapy, immunotherapy, monoclonal antibody and other anti-tumor therapies within 4 weeks before the first dose of the investigational drug, special conditions are as follows:

  1. Including subjects who received oral fluorouracils, small molecule targeted drugs, radiotherapy or traditional Chinese medicines with anti-tumor indications within 2 weeks before the first dose;
  2. Including subjects who received treatment with mitomycin or nitrosoureas within 6 weeks before the first dose;
  3. Including subjects who received cell-based therapy or anti-tumor vaccines within 8 weeks before the first dose.

• Presence of uncontrolled or symptomatic central nervous system (CNS) metastases, or presence of leptomeningeal metastases or spinal cord compression due to metastases before signing the ICF. Exceptions: Subjects with symptomatic CNS metastases who have been treated and radiologically stable (defined as 2 brain images of the same imaging modalities, both acquired after treatment for brain metastases with an interval of at least 4 weeks, showing no intracranial progression by comparison) for ≥ 4 weeks before the first dose of the investigational drug, and have discontinued systemic sex hormone (any dose) therapy for > 2 weeks;

• Subjects with uncontrollable exudate or transudate (thoracic cavity, pericardium and abdominal cavity);

• Subjects with other active malignant tumors within 3 years before being included in the study (from the time of signing ICF), except for the following: basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, prostate cancer in situ, cervical cancer in situ, breast cancer in situ and other malignant tumors that have been treated without disease evidence within > 2 years and do not require continuous treatment; Known to be allergic to the investigational drug or any of its excipient;

• Subjects with current interstitial lung disease, pneumoconiosis, radiation pneumonitis, severely impaired lung function, etc. that may interfere with the monitoring and treatment of suspected drug-related pulmonary toxicity as judged by the investigator;

• Subjects who are unable to swallow and retain oral drugs, or have active gastrointestinal diseases (including inflammatory bowel disease and intestinal obstruction) and other conditions that seriously affect drug absorption as judged by the investigator;

• Subjects who have other serious physical or psychiatric diseases or laboratory test abnormalities that may increase the risk of participating in the study or interfere with the results of the study, and are considered unsuitable for participation in the study by the investigator;