All patients undergo baseline whole-body fludeoxyglucose F 18 (FDG)-PET/CT imaging before beginning chemotherapy. Patients then receive doxorubicin hydrochloride IV, bleomycin IV, vinblastine IV, and dacarbazine IV (ABVD) on days 1 and 15. Treatment repeats every 28 days for up to 2 courses in the absence of disease progression or unacceptable toxicity. Between days 22 and 25 of course 2, patients undergo a second FDG-PET/CT scan to assess response. Subsequent therapy is based on FDG-PET/CT scan results. Patients are stratified according to FDG-PET positivity (yes vs no). Patients who are FDG-PET-negative continue treatment with ABVD for up to 4 additional courses in the absence of disease progression or unacceptable toxicity. Patients who are FDG-PET-positive are then further stratified according to HIV positivity (yes or no) and receive 1 of the following treatment regimens: