Study of MGCD0103 Given Three-Times Weekly in Patients With Advanced Solid Tumors or Non-Hodgkin's Lymphoma

Inclusion Criteria: * Patients must have histologically or cytologically documented advanced or metastatic solid malignancy or aggressive NHL with no reasonable likelihood of achieving clinical benefit with existing therapies, that has failed to respond to standard therapy, has progressed despite standard therapy, or for which no standard therapy exists. Aggressive forms of NHL eligible for the study are: * Burkitt's lymphoma * Mantle cell lymphoma * Diffuse large B-cell lymphoma * Follicle-center cell lymphoma, large cell * Primary mediastinal large B-cell lymphoma * Patients with known central nervous system (CNS) metastases may be enrolled if they have received radiotherapy for their CNS disease, if they have been on a stable dose of steroids for at least 1 month prior to study entry, if they have had computed tomography (CT) or magnetic resonance imaging (MRI) of the brain within 1 month of study entry that shows stable disease and if they are free of neurological symptoms. * Prior therapies allowed: * Cytotoxic therapy * Hormonal therapy/other therapy * Luteinizing hormone releasing hormone (LHRH) agonist therapy * Radiation * Surgery * Adjuvant therapy - Patients may have had unlimited prior adjuvant therapy. A minimum of 28 days must have passed since the end of last treatment and study initiation. Patients must have recovered from any treatment-related toxicities. * ECOG performance status of 0, 1, or 2. * Age ≥ 18 years. * Minimum life expectancy of at least 3 months. * Laboratory requirements Exclusion Criteria: * Patients with a history of another cancer other than basal cell carcinoma or cervical intraepithelial neoplasia (CIN/cervical in situ) unless the previous cancer was treated and the patient has remained disease free for five years or more prior to the current cancer diagnosis. Investigators desiring to enter patients with a second malignancy must discuss with and obtain written approval in advance from the MethylGene Medical Monitor. * Pregnant or lactating women. Women of child-bearing potential must have a negative serum pregnancy test documented within 7 days prior to registration on study. * Patients and their partners, if either are of child-bearing potential, not using adequate birth control measures throughout the course of the study. Both men and women enrolled on study must agree to use a medically acceptable effective form of contraception during the study and for 90 days following the last dose of study medication. An effective form of contraception is an oral contraceptive or a double barrier method, such as condom with diaphragm. * Patients with known meningeal metastasis(es) * Patients with active or uncontrolled infections, or with a fever \> 38.5 degrees Celsius on the day of scheduled dosing * Patients with serious illnesses, medical conditions, or other medical history, including laboratory results, which, in the investigator's opinion, would be likely to interfere with a patient's participation in the study, or with the interpretation of the results * Patients who have been treated with any investigational drug within 30 days prior to study initiation (an investigational drug is one for which there is no approved indication), or who are receiving concurrent treatment with other experimental drugs or anti-cancer therapy * Known hypersensitivity to histone deacetylase (HDAC) inhibitors or any of the components of MGCD0103 * Known HIV or hepatitis B or C (active, prior treated, or both). * Any condition (e.g., known or suspected poor compliance, psychological instability, geographical location, etc) that, in the judgment of the investigator, may affect the patient's ability to sign the informed consent and undergo study procedures.