Brentuximab Vedotin and Nivolumab in Treating Patients With Early Stage Classic Hodgkin Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines. * Eastern Cooperative Oncology Group (ECOG) =\< 2. * Histologically confirmed diagnosis of classical Hodgkin lymphoma (cHL) by current World Health Organization classification (nodular sclerosis, mixed cellularity, lymphocyte rich, lymphocyte depleted, or classical Hodgkin lymphoma, NOS \[not otherwise specified\]) at local enrolling center. Nodular lymphocyte-predominant Hodgkin lymphoma is excluded * Stage IA, IB, IIA, or IIB cHL by Cotswold modified Ann Arbor staging done prior to any treatment with ABVD. * Must have prior to standard of care ABVD treatment at least one lesion that is \> 1.5 cm in the longest diameter on cross-sectional imaging and measureable in two perpendicular dimensions on CT and fludeoxyglucose (FDG) avid by PET. Exclusion Criteria: * Patients must be naive in terms of any prior therapy for Hodgkin lymphoma (including immunotherapy, chemotherapy or radiation therapy) with the exception that they may have received up to 2 cycles of ABVD as standard of care therapy prior to enrollment, as long as they can start protocol therapy (therapy administered in Arms A, B1/B2, or C) within timelines specified by the trial. * Peripheral sensory neuropathy \> grade 1 or any peripheral motor neuropathy. * History of another primary malignancy that has not been in remission for…