This study will consist of a randomized double-blind, placebo-controlled parallel group trial in which 90 participants with AD or MCI receive daily intranasal administrations of either insulin (10 or 20 IU twice a day for a total dose of 20 or 40 IU per day) or placebo (saline twice a day) for 4 months. The study will examine the effects of intranasal insulin administration on cognition, cerebral glucose metabolism, and β-amyloid (Aβ) in cerebrospinal fluid (CSF) and plasma, testing the hypothesis that daily intranasal insulin administration for 4 months will facilitate memory for adults with AD, and adults with mild cognitive impairment (MCI). A subset of participants will have the option to participate in 2 sub-studies: PET scans (prior to and at the end of treatment) to determine whether intranasal insulin increases cerebral glucose metabolism; lumbar punctures (LPs) before and at the end of treatment to determine effects of intranasal insulin administration on CSF Aβ levels.