In the Udana, which is a collections of Buddha's most important utterances, there is the core passage that says "There is an unborn, uncreated... the deathless... nirvana... If there were not... then there would be no liberation." According to the text it was this passage that made his disciples really excited "until the hair on the backs of their necks stood on end."
Buddhism as presented in the West, however, commonly de-emphasizes this central aspect of the teaching. Buddhist apologists like to present the idea that Buddhism teaches that "everything is impermanent" when the fact is that Buddhism teaches liberation from the worldly domain where all is impermanent. There is no classical Buddhist school that teaches otherwise. Different schools have different methodologies and different styles of presentation, but they do not differ on this fundamental point. There is a danger, therefore, that, perhaps in an effort to square Buddhism with reductionist, secular, atheistic scientism, Western apologists of Buddhism will distort the whole Dharmic message to such adegree that it really is not Buddhism any more.
When the Buddha says that sarva samskara anitya ["all samskaras are impermanent"] he is making a contrast with sarva dharma anatma ["all dharma is not self"]. To enter the unborn one must leave the self - one must abandon self-power. To be at one with what the buddhas are at one with one must abandon identification with the transient conceits [samskaras] of one's own fancy and put one's faith in something more reliable. Buddhism offers all manner of different methods to help a person understand this point intellectually, experientially, symbolically, literally, metaphorically, analogically, progressively, suddenly, etc. etc. but unless it is acted upon the whle thing is merely academic.
A formulation that all schools use to typify this act of getting out of the self-power prison and into the orbit of nirvana's liberating influence is the one called Taking Refuge. In Pureland, taking refuge in "what all the Buddhas teach" is expressed as nembutsu. Uttering the nembutsu is affirmation that not everything is impermanent.