Buddhism can be described as defined by it's acceptance of change, called there anicca or impermanence, and considered within that body of thought one of the Three Marks of existence, a core inextricable quality of being which cannot be avoided or ended.
Buddha was a contemporary or near-contemporary of Heraclitus. Buddhist thought avoids the problems of where things begin and end temporarily, by denying any essences or unchanging identities, in another of the Three Marks, anatma, or non-self. In the context of Indian philosophy this a denial of the atma or unchanging soul, the basis in mainstream Sanatana Dharma or Hinduism, for reincarnation - in English Buddhist thought is typically distinguished as describing rebirth instead of reincarnation, and a core metaphor is a candle lighting another candle, that there is a transmission of causes and conditions, not of anything permanent or unchanging. This fits into the wider Buddhist concept of sunyata, or emptiness of inherent nature (in Mahayana Buddhism at least), and the idea of mutually coming to be, interpretation or inter-being, illustrated by the ancient metaphor of Indra's Net.
If everything is in flux, the problem becomes how is there ever any continuity? Buddhist thought relates coming to be, ie the illusion of having a seperate unchanging identity, as coming from the chain of dependent origination, which begins with ignorance about the true nature of things - and who's power is broken by awakening to the true nature of things: becoming an Arahant or a Bodhisattva.
It is a notable contrast to most Western philosophy and religion, that the Buddhist approach is about developing a practice, rather than discovering key truths, or joining with those who share a catechism. Western Buddhist Stephen Batchelor identifies a problem with the standard translation of The Four Noble Truths that are the heart of Buddhist teaching. Typically given as
- dukkha (suffering, incapable of satisfying, painful) is an innate characteristic of existence in the realm of samsara
- samudaya (origin, arising) of this dukkha, which arises or "comes
together" with taṇhā ("craving, desire or attachment")
- nirodha (cessation, ending) of this dukkha can be attained by the
renouncement or letting go of this taṇhā
- magga (path, Noble Eightfold Path) is the path leading to
renouncement of tanha and cessation of dukkha
-Wikipedia
Batchelor shifts the understanding from these as truths to be believed, to recognising them as practices:
The Four Noble Truths are pragmatic rather than dogmatic. They suggest a course of action to be followed rather than a set of dogmas to be believed. The four truths are prescriptions for behavior rather than descriptions of reality. The Buddha compares himself to a doctor who offers a course of therapeutic treatment to heal one’s ills. To embark on such a therapy is not designed to bring one any closer to ‘the Truth’ but to enable one’s life to flourish here and now, hopefully leaving a legacy that will continue to have beneficial repercussions after one’s death." -Confessions of a Buddhist Atheist
The intrinsic unsatisfactorines or anguish of desire is to be seen in our lives, it's causes to be understood, that there is another way is to be recognised, and the eightfold way is the path to be practiced to attain that way.
You didn't ask for specific references, but I felt this presentation of Buddhist thought is likely under-recognised in the West, and provides an additional track to resounding answer so far of 'metaphysics'. There is a tendency tomput the complex and sophisticated thought of Buddhist philosophy in 'the religion box', but in fact many of it's questions, answers, and methods, are directly relatable to the Western tradition of philosophy. The parallels to Stoicism and Stoic practices are striking. And this article identifies a common tactic being used by Nietzsche, Rorty, Wittgenstein, and probably the deepest philosophical thinker in Buddhism & primary influence on Zen, Nagarjuna, nearly two millennia earlier.