A Study to Evaluate the Safety, Tolerability, Pharmacokinetics, Efficacy and Indications of RP903

Inclusion Criteria: * Agreement to provide fresh or archived tumor tissue sample within 3 years * Ia (dose escalation phase and dose expansion phase):patients with pathologically confirmed advanced Malignant solid tumour who have experienced Treatment failure, are unable to tolerate standard treatment, or have no standard treatment * Ib: Patients with advanced malignant solid tumours who have PIK3CA activating mutations, experience treatment failure, are intolerant to standard treatment, or have no standard treatment * Phase Ia: Solid tumour, not limited to specific types; dose expansion phase will prioritize cervix carcinoma, endometrial cancer, ovarian cancer, and breast cancer. * Phase Ib:Cervix carcinoma (Expanded Cohort 1)：Having received first-line (including Platinum-based chemotherapy ± bevacizumab) or second-line treatment and having disease progression during or after treatment; (recurrence during or within 12 months after neoadjuvant or adjuvant treatment in previous treatment will be regarded as one treatment line) * Phase Ib:Endometrial cancer (extension cohort 2)：Progression during or after first-line (including platinum) or second-line treatment of advanced or metastatic disease; (recurrence during or within 12 months after neoadjuvant or adjuvant treatment in previous treatment will be considered as one treatment line)；Sarcoma type not included * Ovarian cancer (expanded cohort 3) (PIK3CA mutation)： * Ovarian cancer, fallopian tube cancer, or primary peritoneal carcinoma who have experienced treatment failure or are intolerant to at least one line of cytotoxic therapy ± PARP inhibitor; (recurrence during or within 12 months after neoadjuvant or adjuvant therapy will be considered one line of therapy) * Pathological types include high-grade serous carcinoma, clear cell carcinoma, or Endometrioid carcinoma * Breast cancer (extension cohort 4) (PIK3CA mutation)： * Advanced, recurrent and metastatic breast cancer; * Prior systemic treatment in at least 1 line and no more than 3 lines (patients who have relapsed during or within 12 months after completion of neoadjuvant/adjuvant endocrine therapy will be considered as one line of endocrine therapy) * At least one measurable lesion as per RECIST v1.1 (except the dose-escalation phase of monotherapy) * Eastern Cooperative Oncology Group (ECOG) performance status score: 0-1 * Adequate hematologic and organ function Exclusion Criteria: * Patients with known allergy to any component of RP903 * Previously treated with PI3K, mTOR or AKT inhibitors * Systemic anti-tumor therapy within 4 weeks prior to the first dose * Presence of leptomeningeal or meningeal metastasis, or presence of signs of carcinomatous Meningitis * Metastases to bone marrow * Child-Pugh grade B or C * Active hepatitis B or C * History of type I Diabetes mellitus，gestational diabetes or uncontrolled type II Diabetes mellitus