It is forbidden to rob or to cheat (i.e., to retain someone's property forcibly even if it was acquired legally), as it says "You shall not cheat your friend and you shall not rob".¹ If one does so he must return what he stole or (if it is no longer intact) pay for it, as it says "And he shall return the thing that he stole [or the thing that he cheated]".² If the person who was robbed dies the goods are returned to his heirs. It is forbidden to buy from a robber; one who does so is like one who buys from a thief.^a

It is forbidden to covet someone's property, as it says "You shall not desire...",³ and there is a special prohibition against inducing him to give or sell it to you, as it says "You shall not covet",^3,4 for coveting leads to robbery, as it says "And they coveted fields and stole".^5,b

If someone owes a person real, movable property and denies it and swears falsely and later confesses he must pay the owner 5/4 of the principal and bring a ram guilt-offering, as it says "If a person... lied to his friend regarding a deposit... or robbery, or cheated his friend, or found lost property and lied about it, and swore falsely... he shall pay it and add a fifth to it... and bring his guilt-offering to Ha-Shem...".⁶ If the owner was a proselyte and dies leaving no heirs the payment is given to the priests on duty, as it says "[They shall confess the sin that they did and pay the guilt and add a fifth to it and give it to the one against whom (they were) guilty;] and if the man has no redeemer to whom the guilt can be returned, the guilt [is] returned to Ha-Shem, to the priest".^7,c

We are forbidden to ignore lost property and we are commanded to return it, as it says "[You shall not see your brother's ox or sheep wandering and ignore them;] you shall return them to your brother... you must not ignore".⁸ Similarly, we are commanded to prevent a loss to someone if it is in our power to do so, as it says "[And thus shall you do] to any loss of your brother's".⁸ If the owner is not known one must advertise what was found and return it to whoever can identify it or prove that it is his. But if it is certain that the owner must have given up hope of recovering it, the finder may keep it.^d

Sources:
1. Lev. 19:13	a. 1:1,4-5; 2:1; 5:1,7; 8:1
2. Lev. 5:23	b. 1:9-11
3. Deut. 5:18	c. 7:1-2,8,14; 8:5-6. On the "fifth" see Shavuos, Note c.
4. Ex. 20:17	d. 11:1,20; 13:1,3; 14:1-4
5. Micah 2:2
6. Lev. 5:2lff
7. Num. 5:6-8
8. Deut. 22:1-3