What's the difference between
свет to mean
world? When would one use one over the other, and are there any set expressions where these are not interchangeable?
When used to mean
свет are synonymous, though the latter can sound somewhat poetic and is more often used in literature and set expressions than in day-to-day life. For example:
на светелучше нету
Чем бродить друзьям
по белу свету
Or to quote the Russian national anthem:
Одна ты на свете
There are other situations where the two cannot be substituted for each other. For instance, one can't use
свет when talking about
the world of ______
«В мире животных»
В мире политики.
Of course, both words also have other meanings which are entirely unrelated (e.g.,
Also note that
мир is used with the preposition
в, whereas свет is used with
Ни за что
Свет usually means not simply "world", but this world as we know it, as the world on Earth populated by people and animals, with all what is going on on it. For example, Asia, Europe, Africa and so on are "части света", or you can refer to the Northern America as "Новый свет".
It also has a somewhat mythological meaning, especially in usages as "произвести на свет" = "give birth", "сжить со свету" = "make someone disappear or even die by treating them badly", "тот свет" = "the other world, the world beyond the grave".
Also, свет has an older meaning "the society". Compare: "выйти в свет" = go out on a public event.
Мир is a more generic notion, it can be used in cases where world means "area" or "region" or "part". See the examples with "of"-preposition given in Philip Seyfi's answer.