1- adj. From the latin for drawn away. Most usages of the term focus on qualitiesof objects, events, phenomena, etc. wich are considered separate or apart from the objects, events or phenomena themselves. Thus, an abstract idea is an intangible one considered apart from specific instances. For example, 'patriotism' is an abstract idea separate from particular patrotic people or events. Note that even when dealing with more concrete things an element of abstraction exists. 'Chair' can be regarded as somewhat less abstract than 'patriotism' although it still may represent an abstract class of chairs devoid of specific attributes. It is probably best to handle the term itself abstractly, relating it to a general dimension that runs from abstract to concrete.
2- vb. The same general notion is found here, i.e. the idea of withdrawal. To abstract is to extract and the cognitive processes involved are neither simple nor well understood. One may absract a simple concept (e.g. 'red' as a property of many red things), an idealization (e.g. 'perfection' as an underlying prototype never found in reality but inducible from many nonperfect examplars), a narrative(e.g.a simple paraphrase capturing the main idea of a story), and so forth.
3- n. In scientific literature, the brief summary of the main ideas of an article, usually given at the very beginning.