Study of Alisertib (MLN8237) in Adults With Aggressive Non-Hodgkin's Lymphoma

Each participant must meet all of the following inclusion criteria to be enrolled in the study:

1. Participant must have histological or cytological diagnosis of a hematological malignancy of the following types that has relapsed or was refractory to prior therapy:

   * Diffuse large B-cell lymphoma
   * Mantle cell lymphoma
   * Burkitt's lymphoma
   * Precursor B-lymphoblastic leukemia/lymphoma
   * T-cell lymphoma, excluding primary cutaneous T-cell lymphoma
   * Transformed follicular lymphoma with ≥ 50% diffuse large cell component.
2. Male or female participants 18 years or older.
3. Eastern Cooperative Oncology Group (ECOG) performance status 0-2.
4. Measurable disease.

Exclusion criteria include the following:

1. Pregnant or lactating females.
2. Known human immunodeficiency virus (HIV) positive or AIDS-related illness.
3. Any serious medical or psychiatric illness that could interfere with the completion of treatment.
4. Total bilirubin ≥ 1.5 × the upper limit of normal (ULN).
5. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≥ 2.5 × the ULN. AST, ALT may be elevated up to 5 times the ULN if their elevation can be reasonably ascribed to their underlying hematological disorder.
6. Absolute neutrophil count (ANC) \< 1,250/mm\^3.
7. Platelet count \< 75,000/mm\^3.
8. Calculated creatinine clearance \< 30 mL/minute.
9. Autologous stem cell transplant less than 6 months prior to enrollment.
10. Participants who have undergone allogeneic stem cell or organ transplantation.
11. Systemic antineoplastic therapy including glucocorticoids (\> 15 mg prednisone/day or equivalent), or treatment with an investigational agent within 14 days preceding the first dose of study drug treatment.
12. Participants who have received treatment with nitrosoureas, mitomycin C, rituximab, alemtuzumab, or other unconjugated antibody treatment, within 12 weeks prior to first dose.
13. Participants who have received treatment with radioimmunoconjugates or within 12 weeks prior to first dose.
14. Participants who have received radiotherapy within 21 days prior to first dose.
15. Myocardial infarction within 6 months of enrollment or current history of New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia.
16. Major surgery within 14 days prior to the first dose.
17. Infection requiring systemic antibiotic therapy within 14 days prior to the first dose or other serious infection.
18. Clinically uncontrolled central nervous system (CNS) involvement.
19. Inability to swallow capsules.
20. History of uncontrolled sleep apnoea syndrome and other conditions that could result in excessive daytime sleepiness (eg, Chronic obstructive pulmonary disease - COPD).