This will be the reading for January 17th. Directions are in the sidebar.
In the Introduction, Hegel described the basic problem of the book, the relation between the subject and the object. Recall the quandary he set up: if (something like) reason is the tool we use to understand the world, then the tool mediates between us and the world. How are we to know the world as it is in itself? If we abstract away the tool, then either we lose the appearances (i.e. the for-us), or the tool was never needed in the first place. Either option seems to leave us blind.
The Phenomenology of Spirit is the long story of how the subject and object can be reconciled, or in other words, how we can have genuine knowledge of the object in-itself, apart from our partial, mediated perspective. One part of the key has been that different forms of consciousness have concerned themselves with different objects: one form of consciousness was concerned with the immediate empirical world, another with the natural sciences, another with the workings of culture. Each time, there has been a different subjective view on a different object.
Another part of the key is that each form of consciousness initially prefers to see its object in an immediate way; it concerns itself with the way the thing appears. This is always carried out in a contradictory way; not a contradiction between subject and object, as if the subject were simply confused, but a contradiction in the way that the subject relates to the object. For example, the ethical form of consciousness saw its world as a harmonious relation between the family and the state, but at the same time required the two elements to be in conflict with one another. That contradiction is what forces the acceptance of a mediated perspective on the object; consciousness has to accept that the initial harmony and the conflict are both of its own doing, a result of its perspective on the object.
Taken together, we can catch a glimpse of what absolute knowing is. Absolute knowing has a new object and a new relation to the object. The object is the mediated relation between the subject and the object itself, and the new relation is the self-conscious awareness of this mediated relationship. So in short: absolute knowing is knowing that the relation between the subject and the object is mediated, and knowing that one knows this.