In Tibetan Buddhism, emptiness is analyzed in many different ways. Madhyamakavatara by Candrakirti lists 16 types of emptiness. These include emptiness of emptiness, emptiness of the unobservable etc. I will not list them all here, but if you are interested you can find detailed explanations in Chandrakirti's Madhyamakavatara with Commentary by Ju Mipham.
While it is utterly impossible to give justice to such deep subject as emptiness in one answer, let me try and mention the most important points.
First, there are the two types of emptiness that represent the crucial distinction between a beginner practitioner's view and an advanced practitioner's view:
- emptiness of self
- emptiness of all dharmas
It is said that beginner practitioners ("hinayana") only understand corelessness of beings (anatta), but still assume various stuff to be objectively/ontologically existing. This results in them erroneously reifying such concepts as the five skandhas, 12 nidanas, 4 noble truths, nirvana, and enlightenment. Advanced practitioners ("mahayana") clearly understand that all knowable phenomena without exception are contextually defined composites.
Another classification scheme I like is the one used by Chogyam Trungpa Rinpoche:
- External Emptiness
- Internal Emptiness
- Absolute Emptiness
External emptiness ("form is emptiness") means: the apparent objects of the so-called physical world are not real entities. There are no real boundaries between objects, and as the time goes and the elements mix and recombine, there are no identities carried over from moment to moment. All objects are imputations of the mind. If we start with any form (a generic object of thought) and engage into analytical decomposition we will never find any stable reference point; everything is defined against of, and in terms of, something else. In other words, phenomenal reality is an illusion, or in modern terminology, what we naively assume to be reality is but an interpretation we make.
Internal emptiness ("emptiness is form") means: and yet, through the power of dependent-coarising, phenomenal reality spontaneously exists. In other words, the illusions are manifestations of the ultimate reality; our mind with its interpretations is a result of beginningless process. Our mind with all its experiences and emotions is but an interplay of forms. So not only all forms are empty imputations of the mind, the mind itself is empty interplay of forms.
Finally, absolute emptiness is the Liberating Realization, what Gotama Buddha called "the final knowledge". According to Chogyam Trungpa, "Absolute emptiness means that there is nothing particularly to do. There is nothing to work on, no one to make a reference point, nothing whatsoever."
Yet another way to explain the same progression is the Four Emptinesses of Completion Stage Meditation:
- Emptiness, experienced when the first five consciousnesses (of sense-organ experiences) dissolve into the sixth (the consciousness of mental experiences).
- Great Emptiness, experienced when the sixth consciousness dissolves into the seventh (emotional consciousness).
- Extreme Emptiness, experienced when the seventh consciousness dissolves into the eighth (ground consciousness).
- Total Emptiness, experienced when the eighth consciousness dissolves into primal wisdom.