This is a phase Ia/Ib, open-label, multiple-dose, dose-escalation and expansion study to evaluate the safety, tolerability, pharmacokinetics and anti-tumor activity of CS1003 in subjects with advanced solid tumors or lymphoma.

Inclusion Criteria:

1. Willing to sign the informed consent.
2. Subjects must have histologically or cytologically confirmed advanced or metastatic solid tumor or unresectable lymphoma and have progressed, are intolerant to, refuse to accept or do not have access to standard therapy.
3. ECOG performance status of 0 or 1.
4. Subjects with evaluable but non-measurable lesion are eligible for Phase Ia. Subjects must have at least one measurable lesion per RECIST Version 1.1 to be eligible for Phase Ib.
5. Archived tumor tissue samples need to be collected, or subjects consent to undergo pre-treatment biopsy if archived sample is not available.
6. Life expectancy ≥ 3 months.
7. Subject must have adequate organ function.
8. Use of effective contraception (males and females).

Exclusion Criteria:

1. Subjects with known symptomatic or untreated brain metastasis or other CNS metastasis.
2. Subjects with active autoimmune diseases or history of autoimmune diseases.
3. Subjects who have to receive glucocorticoids (prednisone at > 10 mg/day or equivalent) or other immunosuppression within 14 days prior to the first dose of CS1003.
4. Subjects with other malignant tumor(s) in the past 2 years are not eligible for Phase Ib
5. Subjects who have received any immune checkpoint treatment, including PD-1, PD-L1, etc.
6. History of HIV infection.
7. Subjects with active Hepatitis B and C infection requiring therapy.
8. Subjects with active infection of tuberculosis.
9. History of organ transplantation.
10. Unresolved toxicities from prior anti-cancer therapy.
11. History of uncontrolled allergic asthma and serious hypersensitive reaction to monoclonal antibodies.
12. Subjects with major cardiovascular diseases.
13. History of alcoholism or drugs abuse.
14. Any condition that, in the opinion of the investigator or sponsor, would jeopardize compliance.