In Group I participants will have an iothalamate glomerular filtration rate (GFR) equal to or greater than 60 ml/min/1.73 m2, and in Group II participants will have a GFR less than 25-59 ml/min/1.73 m2. Both males and females with ADPKD who volunteer and qualify, will be randomly and prospectively assigned to treatment with rapamycin at either a high or low trough blood level or to standard care (each 1/3 of enrolled patients) for one year. The two treatment groups will receive rapamycin doses aimed at maintaining the 20- to 24-hour trough blood levels at either 2 to 5 ng/mL (low-dose), or greater than 5 to 8 ng/mL (high-dose). These trough levels are in the lower range of levels used when treating renal transplant recipients in whom trough levels are typically maintained between 5 and 15 ng/mL.