The seven Principles of Universal Design are often quoted and used in both academic and practical publications.
The 8 Goals of Universal Design aim to operationalise the original 7 Principles to make their application easier to understand. The thinking that went into these goals can be seen in this presentation.
Universal Design is about accepting and celebrating diversity, so there are many ways in which to explain universal design. This list gives a good idea of what it is about – the underpinning philosophy.