Anal HPV infection can be a risk factor for anal cancer, which is a common non-AIDS-defining cancer among HIV-infected MSM. Screening for anal cancer is not widely available and can be difficult to implement. People who receive the FDA-approved quadrivalent HPV vaccine, Gardasil, may have a reduced risk of developing anal HPV infection, which may in turn reduce the risk of developing anal cancer. The purpose of this study is to evaluate the effectiveness of the quadrivalent HPV vaccine, Gardasil, at reducing the incidence of anal HPV infections in HIV-infected MSM and HIV-infected women.