First in Human, Dose Escalation Study of AN4005

Inclusion Criteria: * 1\. Age ≥ 18 years at the time of informed consent and have provided signed informed consent for the trial. 2\. Willing and able to comply with all aspects of the protocol. 3\. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. 4\. Life expectancy ≥ 3 months. 5\. Subjects with histologically or cytologically confirmed advanced solid tumors that are metastatic or unresectable, or relapsed or refractory (r/r) lymphoma, and for whom standard life-prolonging measures are not available. Types of lymphoma may include, but are not limited to, natural killer (NK)/T-cell lymphoma, classic Hodgkin lymphoma (cHL), peripheral T-cell lymphoma (PTCL), and diffuse large B-cell lymphoma (DLBCL). 6\. No standard therapy available or standard therapy is considered unsuitable or intolerable according to the Investigator. 7\. Patients with or without measurable disease are considered eligible. Patients who have measurable disease as assessed by the local site investigator and/or radiologist. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. 8\. Have provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated. If previously treated with anti-PD-1/PD-L1 therapy, tumor tissue sample obtained following the most recent anti-PD-1/PD-L1 therapy is required. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue. For patients with specific types of lymphomas, bone marrow biopsy will be required as appropriate. 9\. Left ventricular ejection fraction (LVEF) greater than 50% on echocardiography or multiple gated acquisition (MUGA) scan. 10\. Patient has organ function as shown by the following: 1. Absolute neutrophil count (ANC) ≥1.5 x 109/L. 2. Hemoglobin ≥8 g/dL (which may be reached by transfusion). 3. Platelets ≥100 x 109/L (which may be reached by transfusion). 4. International normalized ratio (INR) ≤1.5. 5. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤3.0 x upper limit of normal (ULN) or \<5.0 x ULN if liver metastases are present. 6. Total serum bilirubin ≤ ULN or ≤1.5 x ULN if liver metastases are present; or total bilirubin ≤3.0 x ULN with direct bilirubin below or within normal range in patients with well documented Gilbert's Syndrome. Gilbert's syndrome is defined as presence of episodes of unconjugated hyperbilirubinemia with normal results from cells blood count (including normal reticulocyte count and blood smear), normal liver function test results, and absence of other contributing disease processes at the time of diagnosis. 7. Creatinine clearance (CrCL) \>60 mL/min calculated by the Cockcroft-Gault Equation. 11\. A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: <!-- --> 1. Not a woman of childbearing potential Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g., age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) at least six weeks prior to Screening. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow-up hormone level assessment, is she considered not of child-bearing potential. 2. Woman of childbearing potential who agrees to follow contraceptive guidance during the treatment period and for at least 90 days after the last dose of study treatment. Highly effective contraception is defined as either: * Total abstinence: When this is in line with the preferred and usual lifestyle of the patient. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) * Female sterilization: When the female study patient has had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow-up hormone level assessment. * Male partner sterilization (with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate). For female study patients, the vasectomized male partner should be the sole partner for that patient. * Using a combination of any two of the following: * Placement of an intrauterine device (IUD) or intrauterine system (IUS), and * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository. * Hormonal contraception methods (e.g., oral, injected, implanted). 12\. A male participant must agree to use contraception during the treatment period and for at least 90 days after the last dose of the study treatment. Exclusion Criteria: 1. Have been discontinued treatment due to a Grade 3 or higher immune-related AE (irAE) from prior anti-PD-1or anti-PD-L1 therapy, or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137). 2. Have received prior systemic anti-cancer therapy including investigational oncology agents within 4 weeks or 5 half-lives, whichever is shorter. Note: Participants must have recovered from all AEs due to previous therapies to ≤ Grade 1 or returned to baseline. Participants with ≤ Grade 2 neuropathy or alopecia may be eligible. 3. At least 6 weeks must have elapsed since CAR-T infusion and subjects must have experienced disease progression, and not have residual circulating CAR-T cells in peripheral blood (based on local assessment). Any encountered treatme