Inclusion criteria  Age ≥ 18 years  Subjects with histological- or cytological-confirmed, advanced cancer who have progressed on (or not been able to tolerate) standard therapy or for whom no standard anticancer therapy exists  For Phase 1, all tumor types may be enrolled For Phase 2, subjects will be enrolled as per the study design section above ECOG performance status of 0 or 1 Women of childbearing potential (WOCBP) must have a negative pregnancy test (urine or serum) within 7 days prior to starting the study drug. Both males and females must agree to use effective birth control during the study (prior to the first dose and for 6 months after the last dose) if conception is possible during this interval. Subjects must be able to swallow and retain orally administered medication and not have any clinically significant GI abnormalities that may alter the absorption, such as malabsorption syndrome or major resection of the stomach or bowels. Able to agree to and sign t he informed consent and to comply with the protocol.  Exclusion criteria  Subjects with a history of brain metastases or who have signs/symptoms attributable to brain metastases and have not been assessed with radiologic imaging to rule out the presence of brain metastases. Subjects with treated brain metastases that are asymptomatic and have been clinically stable for at least 4 weeks will be eligible. Subjects who have not received vaccines for SARS-COV-2 within last 3 months and have suspected signs and symptoms of COVID-19 or a recent history (within 14 days) of contact with any COVID-19 positive subject/isolation/quarantine or subjects with confirmed COVID-19.  Subjects with a history of another primary malignancy, other than:  Carcinomas in situ, e.g., breast, cervix, and prostate Locally excised nonmelanoma skin cancer No evidence of disease from another primary cancer for 2 or more years and has not taken any anti-cancer treatment in 2 years. Any other clinically significant acute or chronic medical or psychiatric condition or any laboratory abnormality that may increase the risk associated with study drug administration or may interfere with the interpretation of study results. Diseases that significantly affect GI absorption of fadraciclib. Subjects who have impaired cardiac function or clinically significant cardiac disease. Presence of active chronic inflammatory bowel disease (ulcerative colitis, Crohn's disease) or GI perforation within 6 months of enrollment Presence of an active infection requiring intravenous antibiotics Presence of known history of human immunodeficiency virus-1/2 with uncontrolled viral load and on medications that may interfere with metabolism Presence of active hepatitis B virus (HBV) or hepatitis C virus (HCV). Chemotherapy, biologic therapy, targeted therapy, immunotherapy, extended-field radiotherapy, or investigational agents within 5 half-lives or 3 weeks (whichever is shorter) prior to administration of first dose of study drug on Day 1 or have not recovered from the side effects of such therapy. Major surgery/surgical therapy for any cause within 4 weeks of the first dose