Study of AXT-1003 in Subjects With Advanced Malignant Tumors.

Inclusion Criteria: 1. For Ia dose escalation part only: R/R NHL: Locally histopathological diagnosis of relapsed/refractory non-Hodgkin lymphoma (R/R NHL), who have progressed or been intolerant after the available standard therapies, or have no access to the standard therapies. Advanced solid tumors: Locally histopathological diagnosis of locally advanced unresectable and metastatic solid tumors,The above subjects have progressed or been intolerant after the available standard therapies, or have no access to the standard therapies. For Ib dose expansion part only: Subjects with relapsed/refractory peripheral T-cell lymphoma (R/R PTCL) 2. Eastern Cooperative Oncology Group (ECOG) performance status scale 0 to 1. 3. Have a life expectancy of at least 3 months. 4. For Ib dose expansion part and not mandatory for Ia dose escalation part: Subjects with R/R NHL must have measurable lesions as defined by Lugano 2014 criteria. Subjects with advanced solid tumors must have measurable or evaluable lesions as defined by RECIST 1.1. 5. Adequate organ and bone marrow functions. 6. The adequate washout period for prior therapy . 7. Subjects must use a highly effective contraception method throughout the study and for 3 months after discontinuation of the study drug. 8. Signed ICF and willing to comply with all the requirements in the protocol. Exclusion Criteria: 1. Diagnosis of precursor B-cell lymphoblastic leukemia/lymphoma, precursor T-cell lymphoblastic leukemia/lymphoma, precursor NK cell lymphoblastic leukemia/lymphoma. Diagnosis of chronic lymphocytic leukemia (CLL), small lymphocytic lymphoma (SLL). 2. Central nervous system infiltration. 3. Uncontrolled or significant cardiovascular disease. 4. Major surgery within 4 weeks before the first dose of study drug. 5. Known or suspected hypersensitivity to AXT-1003 or any of the excipients. 6. Inability to take oral medication, or malabsorption syndrome or any other uncontrolled gastrointestinal condition (e.g., nausea, diarrhea, or vomiting) that might impair the bioavailability of AXT-1003. 7. History of other malignancies prior to enrollment; except for subjects with basal cell carcinoma of skin, squamous cell carcinoma of skin, cervical carcinoma in situ, or other carcinomas in situ who have undergone possible curative treatment and do not have disease recurrence within 5 years since starting the treatment. 8. Any prior treatment-related clinically significant toxicities that have not resolved to Grade ≤ 1 or prior treatment-related toxicities that are clinically unstable and clinically significant at time of enrollment. 9. Active infection requiring systemic treatment. 10. Infection with hepatitis B virus with positive hepatitis B surface antigen, or hepatitis C virus with detectable anti-hepatitis C circulating viral RNA. 11. Subjects known to be infected with human immunodeficiency virus and active tuberculosis. 12. Females who are pregnant or breastfeeding.