Inclusion Criteria:
* Having signed the written Informed Consent Form (ICF);
* Male or female aged ≥18 years;
* Life expectancy ≥12 weeks;
* Eastern Cooperative Oncology Group (ECOG) Performance Score 0 or 1;
* Patients with histologically or cytologically confirmed locally advanced or metastatic breast cancer, ovarian cancer, prostate cancer or other advanced solid tumors who have experienced disease progression, and available SOC therapies had been exhausted;
* be willing to provide tumor tissue samples (fresh frozen \[SF\] or previously retained paraffin-embedded \[FFPE\] tumor tissue samples) or peripheral blood germline DNA or ctDNA sample to detect BRCA mutation, or other deficiency in the HR pathway (by the detection method of next generation sequencing \[NGS\])
* At least one measurable lesion according to RECIST v1.1;
* No serious hematological, cardiopulmonary, or liver or kidney diseases other than the primary disease;
* Adequate organ function and bone marrow function.
Exclusion Criteria:
* Previous or current use of POLQ inhibitors;
* Hypersensitivity to the active pharmaceutical ingredient or any excipient of SYN818;
* Central nervous system (CNS) metastasis or meningeal metastasis with clinical symptoms, or other evidence indicating that CNS metastasis or meningeal metastasis has not been adequately controlled;
* Other malignant tumors than the study tumors within 5 years prior to the first dose of the study drug, except for localized cancers that have been evidently cured or disease-free for at least 3 years, such as basal or squamous cell skin cancer, superficial bladder cancer, prostate carcinoma in situ, carcinoma in situ of cervix, or carcinoma in situ of breast;
* Patients with Myelodysplastic syndrome (MDS)/Acute myeloid leukemia (AML) or with features suggestive of MDS/AML;
* Dysphagia or refractory nausea and vomiting, malabsorption, extracorporeal biliary shunts, or gastrointestinal disorders that affect drug absorption, e.g., Crohn's disease, ulcerative colitis, or short bowel syndrome, or other malabsorption conditions;
* Major surgery or serious trauma within 4 weeks prior to the first dose of the study treatment or major surgery planned during the trial period, and none of the AEs related to surgery or major trauma have resolved (to ≤ CTCAE v5.0 Grade 1 or baseline level) before the first dose of the study drug;
* History of use within 2 weeks prior to the first dose of the study treatment and need to use protocol-prohibited potent inhibitors or potent inducers of cytochrome P450 (CYP) 3A4/BCRP/P-gp during the study;
* Serious systemic diseases or laboratory abnormalities or other conditions that, at the Investigator's discretion, will make it unsuitable for the patient to participate in this clinical trial.
