This study is designed to observe the immune system response during the first year after kidney transplant. Cells of the immune system in the recipient's blood, urine, and transplanted kidney will be tested to observe how the drugs used to prevent rejection influence them, if these cells change over time, and if they are related to kidney rejection. The comparisons will allow researchers to study how the developing immune system interacts with the kidney transplant. Blood from the kidney donor will be requested so that researchers can study how the recipient's immune system interacts with donor cells.