This trial will accrue in six cohorts; Arm 1, patients with cutaneous T-cell lymphoma who have had less than or equal to two prior cytotoxic chemotherapy regimens; Arm 2, patients with peripheral T-cell lymphoma who have had less than or equal to two prior cytotoxic chemotherapy regimens; Arm 3, patients with cutaneous and peripheral T-cell lymphoma who have had more than two prior cytotoxic chemotherapy regimens; Arm 4, patients with other mature T-cell lymphomas; Arm 5, a replicate arm of arm 1; Arm 6, patients with peripheral T-cell lymphoma who have had more than two prior cytotoxic chemotherapy regimens; Arm 7, patients with cutaneous T cell lymphoma who have received vorinostat.