Alzheimer's disease is not a normal part of aging. It is a disease. While it is true that growing older increases your risk for developing AD, it does not mean that you will develop AD. We now know that changes in the brain's structure and neurochemical system occur with age, and that these changes may affect aspects of thinking and memory. However, these age-related changes are considered normal and do not represent AD.
With age, nerves and other tissues in the brain are lost or shrink, causing the brain to shrink in size. As nerves die or function less effectively, the availability of various neurotransmitter systems or chemical neurotransmitters (i.e., chemical substances in the brain which allow the nerves to communicate with each other) may diminish. Consequently, this may or may not result in observable but often subtle, age-related cognitive changes, including more difficulty recalling names or proper nouns, slowed processing speed, or the need for more time or more repetitions to learn new information.
What is not a normal part of aging is forgetfulness. Research shows that older adults are capable of learning new information as well as younger adults if given more time to learn and a greater number of learning "trials". While it may take longer to retrieve the information that has been learned, once learned, it is not forgotten.