Ciao Max

To steal, to rob, to thieve all mean basically the same, ie: to take some money or some item that belongs to somebody else, a person or a business such as a shop.

To rob is usually used more for maybe a bank, we call a person who takes money from a bank a 'bank robber' 

If a person has their wallet or watch or bag taken, we would usually say 'my wallet has been stolen.' If using 'to rob' we would say 'I have been robbed' rather than 'my wallet has been robbed.' 

There is also 'to burgle.' If someone has had their house broken into, they might say 'We have been robbed', but more likely for example 'we've been burgled and they have stolen the computer.' A person who breaks into someone's house to steal is called a burglar. 

Thieve is used much less often as a verb, . Theft is not a verb, theft is a noun, for example 'there has been a theft at the shop'

Thief is also a noun. Someone who thieves or steals or robs is a thief. 

To mug implies some violence has been used rather than just theft, and usually refers only to an attack in the street, not a theft from a house or a shop. Someone who has been attacked in the street and had their money stolen, for example, has been mugged. 

 spero che ti ho aiutato.