Inclusion Criteria:

• Age ≥ 18 years.
• Histologically confirmed diagnosis of classical Hodgkin's lymphoma or NHL (follicular, DLBCL, or mantle cell) and confirmed relapsed or refractory disease. 1)Subjects with a diagnosis of classical Hodgkin's lymphoma MUST have relapsed following a prior autologous, allogeneic or reduced intensity allogeneic stem cell transplant. Subjects who received an allogeneic transplant must have no evidence of graft versus host disease (GVHD), and have discontinued treatment with immunosuppressive agents ≥ 3 months prior to enrollment in this study. 2)Subjects with DLBCL must be ineligible for, or have refused, autologous stem cell transplant, or have relapsed following transplant. 3)Subjects with MCL must have relapsed after prior treatment and not be eligible for autologous stem cell transplant (ASCT) or have relapsed following ASCT. 4)Subjects with NHL who may have received a prior allogeneic stem cell transplant must have no evidence of GVHD, and have discontinued treatment with immunosuppressive agents ≥ 3 months prior to enrollment in this study.
• Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2 Evidence of measurable disease (ie, at least one lesion that can accurately be measured in at least two dimensions as ≥15 mm with spiral CT scan). 1)If only single target lesion must be PET positive, and measure ≥20mm in two dimensions (required only for subjects with Hodgkin's lymphoma and DLBCL).
• Adequate organ function including: 1)Absolute neutrophil count (ANC) ≥ 1.5 x 10^9/L (≥1500/mm^3); and 2)Platelets ≥ 50 x 10^9/L (≥50,000/mm^3); and 3)Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (unless increased due to Gilbert's Syndrome or hemolysis); and 4)AST (SGOT) and ALT (SGPT) ≤ 2.5 x ULN; and 5)Serum creatinine ≤ 1.5 x ULN.
• At least 3 weeks elapsed since any prior anticancer therapy (standard or investigational) and full recovery (NCI CTCAE grade 1) from the toxic effects of that treatment.
• For women of childbearing potential, a negative serum pregnancy test within 7 days of treatment, a negative urine pregnancy test immediately prior to the first treatment with study drugs, and use of 2 physician-approved methods of birth control throughout the study and for a period of 3 months following the study.
• Written informed consent, willingness, and ability to comply with all study procedures.

Exclusion Criteria:

• Prior HDAC inhibitor and azacitidine combination therapy.
• Known hypersensitivity to azacitidine, HDAC inhibitors, and/or any components of MGCD0103, FB-MGCD0103, or TA-FB-MGCD0103 capsules and or azacitidine formulation components.
• Any condition that will put the subject at undue risk or discomfort as a result of adherence to study procedures (eg, requirement to take MGCD0103 with Gatorade®).
• Previous or concurrent malignancy except adequately treated basal cell or squamous skin cancer; in situ carcinoma of the cervix, or other solid tumor treated curatively, and without evidence of recurrence for at least 3 years prior to study entry.
• Presence of significant involvement of the liver by lymphoma and impaired synthetic function as indicated by hypoalbuminemia of < 1.0 x LLN.
• Active and uncontrolled clinically significant infection.
• Known Hepatitis B surface antigen (HepB SAg) positive or Hepatitis C antibody positive.
• Known infection with human immunodeficiency virus (HIV).
• History of melena or hematemesis within the last 3 months.
• Known central nervous system metastases.
• Less than 4 weeks elapsed since any major surgery.
• Pregnant or lactating women. Women of child-bearing potential (WOCBP) must have a negative serum pregnancy test within 7 days of beginning Part 1 of the study.
• WOCBP and men whose partners are WOCBP must use two acceptable methods of contraception while enrolled in this study, and for a period of 3 months following study drug treatment. Subjects unwilling or unable to follow this guideline will be excluded.
• Concurrent chronic treatment with therapeutic doses of systemic steroids.
• Prior or active disease or conditions that, in the opinion of the investigator, may interfere with the procedures or evaluations to be conducted in the study. This includes, but is not limited to, uncontrolled intercurrent illnesses such as symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situation that would limit compliance with study requirements.