Dementia is a chronic, progressive brain disease that may involve a number of symptoms, including memory loss and changes in personality, behavior, judgment, attention span, language and thought. The most common type of dementia is Alzheimer's disease. Over time, patients with Alzheimer's disease may lose the ability to perform daily tasks related to personal care (for example, bathing, dressing, and eating) and may be unable to handle money or travel to familiar places. Previous clinical trials have shown that a twice-daily dose of galantamine (18 - 32 mg/day) improved symptoms of Alzheimer's disease. This multicenter, double-blind, placebo-controlled study evaluates the safety and effectiveness of a controlled-release form of galantamine in patients with Alzheimer's disease. All patients receive placebo during the first month of the study. Patients then receive controlled-release galantamine (8 - 24 mg once daily), or immediate-release galantamine (4 - 12 mg twice daily) or placebo for 6 months. The dose of galantamine starts at 8 mg/day and may be increased up to 24 mg/day, if needed. The dose may be adjusted up or down during the first 12 weeks of double-blind treatment based upon effectiveness and tolerability. Patients continue to receive the dose they are taking at the end of 12 weeks for the remainder of the study. The primary measures of effectiveness include the change from baseline to the end of treatment in the ADAS-cog/11 (Alzheimer's Disease Assessment Scale: sum of 11 cognitive items) and CIBIC-plus (Clinician's Interview Based Impression of Change - Plus Caregiver Input) scores. Additional measures of effectiveness include the change from baseline in the Alzheimer's Disease Cooperative Study - Activities of Daily Living (ADCS-ADL) and the Neuropsychiatric Inventory (NPI) scores. Safety evaluations (incidence of adverse events, electrocardiograms (ECGs), physical examinations, laboratory tests) are performed throughout the study. Patients who complete the double-blind portion of the study have the opportunity to receive galantamine in an open-label follow-up study. Patients may also participate in an optional portion of the study in which their genetic material is analyzed to see if contains something that would affect the way galantamine is used by their bodies. The study hypothesis is that treatment with controlled-release galantamine is effective in improving the symptoms of Alzheimer's disease and is well tolerated. Controlled-release galantamine 8 - 24 mg by mouth once daily, or immediate-release galantamine 4 - 12 mg by mouth twice daily, or placebo. Dosing starts at 8 mg/day and may be increased up to 24 mg/day, if needed. The study duration is 6 months.