The proposed Studies will examine the effects of intranasally administered long-acting insulin detemir on cognition and cerebrospinal fluid (CSF) markers of AD pathology and inflammation in persons with Alzheimer's disease (AD) or its prodrome, amnestic mild cognitive Impairment (aMCl). The rationale for these studies is derived from growing evidence that insulin contributes to multiple brain functions, and that insulin dysregulation can contribute to AD pathogenesis. Thus, therapies aimed at restoring normal insulin signaling in CNS may have beneficial effects on brain function. Intranasal administration of Insulin increases insulin signaling in brain without raising peripheral levels and causing hypoglycemia. Insulin detemir is an insulin analogue that may have better action in brain than other insulin formulations because of its albumin binding properties. We will test the therapeutic effects of intranasally-administered insulin detemir in two studies: 1) an initial dose-finding study in which participants will receive one of three doses of insulin detemir or placebo for a three week period; and 2) a four-month randomized, double-blind pilot trial comparing the effects of regular insulin, the optimal dose of insulin detemir determined in study 1, and placebo. We will test the hypothesis that treatment with intranasal Insulin or insulin detemir will improve memory and daily functioning in persons with AD/aMCI, but that greater effects will be observed for insulin detemir. Participants will also undergo lumbar puncture (LP) before and at the end of treatment to measure changes in CSF B-amyloid (AB), tau, and inflammatory markers.