The current proposal is to conduct a study using a battery of neuropsychological tests capable of detecting the broad range of cognitive difficulties associated with relapsing remitting multiple sclerosis. This study will compare cognitive functioning over time of patients receiving alemtuzumab. The study will also compare the change in cognitive functioning over time to that of relapsing remitting multiple sclerosis patients receiving interferon beta-1a and normal controls enrolled in a parallel study conducted by Wilken et al.To evaluate cognitive effects of alemtuzumab, the investigators will perform neurological exams and brain scans and will administer questionnaires to measure the severity of multiple sclerosis, how well subjects are functioning, how they are feeling, and to find out about what other medical visits subjects may have had during the study. Neurological testing in this study will require the subject to perform relatively simple tasks to evaluate their multiple sclerosis. These tasks include a five hundred meter walk, a timed twenty five foot walk, a nine hole peg test, an eye exam, and a test requiring you to add small numbers in your head quickly. The brain scans will involve Magnetic Resonance Imaging and are painless, except for injection of a contrast agent called gadolinium, which is necessary to detect areas in the brain where their MS may be currently active. Magnetic Resonance Imaging is widely used to diagnose and assess patients with multiple sclerosis. All patients will be required to return to their study site every 3 months for assessments and testing. In addition, safety-related blood tests will be performed at least monthly. If their blood test results become abnormal, they may have to have blood tests taken more frequently, in some cases weekly, until test results improve. Monthly blood tests should be performed at your study site, but if subjects are unable to return to the study site for the blood testing, they may be able to use a local laboratory.