Mature B-Cell Lymphoma And Leukemia Study III

Inclusion Criteria: St. Jude participants and collaborating sites participating in therapeutic and biological objectives: 1. Participant must have a histologic diagnosis of a mature B cell lymphoma (e.g., Burkitt lymphoma/leukemia, atypical Burkitt lymphoma, diffuse large B-cell lymphoma, mediastinal large B-cell lymphoma, mature B-cell lymphoma NOS) as defined in the WHO classification. 2. Participant must be previously untreated, (no more than 72 hours of steroids, one intrathecal chemotherapy treatment, and/or emergency radiation). 3. Participant must be \< 22 years of age at the time of diagnosis 4. For selected higher-risk CD20+ Group B and all CD20+ Group C participants receiving rituximab only (e.g., those with MLBLC, Stage III with LDH ≥ 2 times upper limit of normal (ULN), and/or bone marrow/CNS involvement: All participants who will receive rituximab must have hepatitis screening prior to enrollment. Participants whose results indicate that they are carrier of hepatitis B can still be treated per Group B or C but will NOT receive rituximab. This screening must be done for eligibility for participants who will receive rituximab, BUT the results are not needed prior to enrollment: * Hepatitis B immunization status (vaccination Yes or No) * HBsAg * Anti-HBs antibody * Anti-HBc antibody. 5. All participants must have screening prior to enrollment; participants whose results indicate that they are carrier of hepatitis B can still be treated per group B and C but will NOT receive rituximab 6. HIV test has been obtained within 42 days. Participants who test positive for HIV cannot be enrolled on therapeutic part of study, but are still eligible for biology studies. 7. Informed consent must be obtained according to St. Jude guidelines before enrollment into study. Participants from Collaborating Sites Participating in Biological Objectives Only: 1. Participant must have a histologic diagnosis of a mature B cell lymphoma (e.g., Burkitt lymphoma/leukemia, atypical Burkitt lymphoma, diffuse large B-cell lymphoma, mediastinal large B-cell lymphoma, mature B-cell lymphoma NOS) as defined in the WHO classification. 2. Participant must be \< 22 years of age at the time of diagnosis. 3. Participant must be previously untreated (no more than 72 hours of steroids, one intrathecal chemotherapy treatment, and/or emergency radiation) at the time of the diagnostic biopsy. 4. Informed consent must be obtained by local PI or his/her designee according to ICH/Good Clinical Practice and local guidelines before enrollment into study. Exclusion Criteria: Participants from Collaborating Sites Participating in Therapeutic and Biological Objectives: 1. Participants known to be HIV positive (for therapeutic part of protocol, HIV participants are eligible for biology studies). 2. Participants who are pregnant or lactating. 3. Inability or unwillingness of research participant or legal guardian to consent. Participants from Collaborating Sites Participating in Biological Objectives Only: 1. Inability or unwillingness of research participant or legal guardian to consent. 2. Histologic diagnosis other than a mature B-cell lymphoma as defined in the WHO classification.