Inclusion Criteria:

          1. Have given written informed consent prior to any study specific procedures.

          2. Male or female, aged ≥18 years.

          3. Subjects with advanced solid tumors:

               -  Phase 1: Histologically or cytologically confirmed, locally advanced (not
                  amenable to curative treatment of surgical resection or radiation therapy),
                  recurrent, or metastatic solid tumors that were refractory to standard therapy or
                  for which no standard-of-care therapy.

               -  Phase 2a Cohort A: HR+/HER2- locally advanced, recurrent, or metastatic breast
                  cancer with disease progression after first-line endocrine therapy (not
                  fulvestrant) or intolerant of it, histologically confirmed by the primary and/or
                  metastatic lesions, not amenable to chemotherapy or curative treatment of
                  surgical resection or radiation therapy; if the pathology of the primary and
                  metastatic lesions are inconsistent, diagnosis should be based on metastatic
                  lesions' pathology.

               -  Phase 2a Cohort B: HR+/HER2- locally advanced, recurrent, or metastatic breast
                  cancer with no prior systemic therapy in this disease setting or relapse more
                  than 1 years from completion of adjuvant endocrine therapy, histologically
                  confirmed by the primary and/or metastatic lesions, not amenable to chemotherapy
                  or curative treatment of surgical resection or radiation therapy; if the
                  pathology of the primary and metastatic lesions are inconsistent, diagnosis
                  should be based on metastatic lesions' pathology.

          4. At least 1 measurable lesion based on the RECIST v1.1 criteria.

          5. Life expectancy≥ 12 weeks.

          6. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS)≤1.

          7. Adequate bone marrow and organ function, defined as following:

               1. absolute neutrophil count≥1.5×10^9/L, platelets≥100×10^9/L, hemoglobin≥100 g/L;

               2. total bilirubin≤1.5×ULN(≤3×ULN for Gilbert syndrome), alanine aminotransferase
                  and aspartate aminotransferase≤3×ULN;

               3. serum creatinine≤1.5×ULN or a creatinine clearance calculated by Cockcroft-Gault
                  formula≥50 mL/min; urinary protein measured by semi-quantitative method<2+; if
                  urinary protein measured by semi-quantitative method at baseline ≥2+, 24-h
                  urinary protein<1g;

               4. activated partial thromboplastin time and international normalized ratio≤1.5×ULN;

               5. LVEF≥50%;

               6. Corrected QT interval (QTcF)<450ms for men and <470ms for women at resting.

          8. Female subjects should take effective contraceptive methods during the study and for
             60 days after the last dose of BPI-1178, and must have a negative pregnancy test prior
             to dosing if of child-bearing potential, or must have evidence of non-child-bearing
             potential; male subjects should take effective contraceptive methods during the study
             and for 120 days after the last dose of BPI-1178.

          9. All subjects must have enough mental behavior ability, understand the nature and
             significance of the study, as well as the risks associated with the study.

        Exclusion Criteria:

          1. Currently receiving or have received any CDK4/6 inhibitors.

          2. Have had allergies or history of severe allergies.

          3. Have participated in any clinical trials within 4 weeks prior to the dosing of
             BPI-1178.

          4. Have received last dose of anti-cancer treatment (chemotherapy, endocrine therapy,
             targeted therapy, immunotherapy or embolization therapy, etc.) within 4 weeks prior to
             the dosing of BPI-1178; have received last dose of biological products (if endocrine
             therapy, within 4 weeks prior to the dosing of BPI-1178), nitrosourea or mitomycin C
             within 6 weeks prior to the dosing of BPI-1178; (except GnRHa treatment for
             pre/peri-menopausal subjects in phase 2a study).

          5. Any toxicity related to previous treatment before enrollment defined by CTCAE (v5.0)
             Grade≥2 (except hair loss).

          6. Presence of third interstitial fluid that cannot be controlled by drainage or other
             methods (such as large amounts of pleural fluid and ascites).

          7. Requiring long-term treatment of steroid.

          8. Having uncorrectable hypokalemia and hypomagnesemia at enrollment.

          9. Any of the following criteria: any cardiac rhythm and conduction abnormalities with
             clinical significance, such as atrial fibrillation, complete left bundle branch block,
             3rd-degree atrioventricular block, 2nd-degree atrioventricular block, PR
             interval>250ms; any risk of QT interval prolongation and arrhythmia, such as
             symptomatic heart failure-New York Heart Association (NYHA) grades II～ IV, congenital
             long QT syndrome, Brugada syndrome, history of QT interval prolongation (male>470ms,
             female>480ms) or history of torsade de pointes, family history of long QT syndrome or
             sudden death with unknown cause before 40 years old in the first-degree relatives, any
             concomitant medications that may prolong QT interval; any following diseases within 6
             months prior to the dosing of BPI-1178: unstable angina pectoris, myocardial
             infarction, coronary heart disease, cerebrovascular events, pulmonary embolism, or
             cardiac revascularization,etc..

         10. Have active infection, such as hepatitis B (HBsAg positive and hepatitis B virus
             DNA≥1×10^3 copy/ml), hepatitis C and human immunodeficiency virus (HIV) infection.

         11. Have a history of allogeneic organ transplantation and allogeneic hematopoietic stem
             cell transplantation.

         12. Any factors, in the judgment of the investigator, that may affect the administration
             and absorption of BPI-1178 (for example, uncontrolled inflammatory gastrointestinal
             diseases, abdominal fistula or gastrointestinal perforation within 6 months, extensive
             resection of small intestinal, with tube feeding or parenteral nutrition, inability to
             swallow, chronic diarrhea, and intestinal obstruction).

         13. Have spinal cord compression, metastases of the meninges, or brain metastases with
             obvious symptoms. The following cases of brain metastases without symptoms can be
             enrolled: brain metastases without obvious symptoms diagnosed at screening visit,
             steroids and/or local treatment not required judged by investigator; brain metastases
             without obvious symptoms after local treatment (such as radiotherapy), and steroids
             and/or antiepileptic therapy has stopped for at least 7 days before the first dosing
             of BPI-1178.

         14. In the judgment of the investigator, have a concomitant disease (such as severe
             hypertension, diabetes, thyroid disease, severe infection, portal hypertension,
             cirrhosis, etc.) that would endanger the subjects' safety or affect the completion of
             the study.

         15. Have had major surgery (craniotomy, thoracotomy, or laparotomy) or unhealed wounds,
             ulcers, or fractures within 4 weeks prior to the dosing of BPI-1178.

         16. Pregnant or lactating women, or fertile women with pregnancy test positive at
             baseline.

         17. Any factors that may endanger subject's safety and may affect subject's compliance
             with the study.

         18. Drug abuse, alcoholic addiction, medical and mental illness and social barriers judged
             by investigator, which may interfere the subjects' participation in the study or
             affect the evaluation of study endpoints . Any factor that investigator believes may
             make the subjects not suitable to receive BPI-1178. Subjects are unwilling or unable
             to comply with the requirements of the study protocol.