halacha - Is taking public property or abandoned belongings considered stealing?

Let's say a person moves out and leaves some belongings (for instance food, books, other personal items) for public consumption - be it with or without a note that it is for free (why would anyone put his things out like that if not for the purpose of giving it away). But also another example: There is a good knife in one drawer that is in a public kitchen. It is not closed and after I take and use it, I return it in the next morning after washing/cleaning it into its respective drawer.

Living in my current environment it is bound to happen that some things just lay around 'for free'. Am I free to take these things (and maybe, once they served their use e.g books, recyclable items) and offer them for free back again?

What does Chazal say about this. I'm sure that back in those days where there was probably much less privacy and 'private enclosed property' than nowadays, this issue must've been discussed somewhat extensively.

Answer

BusinessHalacha.com has a wonderful series called "Lost and Found", well worth checking out.
"Lost & Found #8" seems to address your question:

The Gemara (Bava Metzia 25b; 31a) teaches that when someone is careless with his property and knowingly leaves it in an insecure place, it is called aveidah midaas (knowing loss) and you are not required to do hashavas aveidah (Shulchan Aruch, Choshen Mishpat 261:4).

Nonetheless, the Shulchan Aruch writes that the item does not become hefker (ownerless). Although you are not required to collect and return said property, you may not take them for yourself. The Tur and Rema write, on the other hand, that a person who recklessly abandons his items renders them hefker and you may take them.

BusinessHalacha.com continues:

Machane Ephraim (Hil. Zechiyah Mihefker #6) explains that this depends on the evaluation of the circumstances. For example, if the items were old and worn, they certainly would be hefker, whereas items in good condition would depend on this dispute (see Pischei Choshen, Aveidah 4:12).

If the items were not abandoned, even if not left securely, e.g. a can of balls was left in the locker room, they do not become hefker.

See also: "Lost & Found # 20", "#35", "#38 (summary)"