The main difference is 'never' means "at no time", and 'ever' means "at any time".

As Greg says, 'ever' means at 'any time', while 'never' means 'at no time'. 'Ever' is the positive flipside of 'never'. I realise that this is a difficult concept for many learners to get their heads around, as the any/no duality does not correspond to equivalents in other languages. In Italian, both concepts would be translated as 'mai'. So translation does not help. Don't try to translate. A few things to bear in mind, though: 1. The difference between 'ever' and 'never' is the same as the difference between 'anybody' and 'nobody', 'anything' and 'nothing' and so on. If you can get the idea of the the difference between these pairs of words, this will help you to understand how 'ever' relates to 'never'. 2. Try to think of 'ever' - as well as anybody, anywhere, anything and any - as being OPEN possibilities. They are open because they include the possibilities of of all the positive options as well as the negative one. By contrast, the negative words ( never, nobody and so on) refer to a single negative fact, and in that respect, we can think of them as referring to a 'closed' possibility. For example: 'Have you ever been to London?' When we ask this, we have in mind several possibilites ( that the person went to London when they were a child, when they were a teenager, when they were an adult...or never. The concept of 'ever' or 'any time' is open to both positive and negative possibilities). 'Never', on the other hand, only refers to a negative concept. 3. Remember that standard English grammar follows the mathematical convention of one negative and one positive making a negative, and two negatives making a positive. This means that there are often two ways of saying the same thing: I have no money = I haven't any money I never lie = I don't ever lie

I understand the possible confusion here because 'mai' is often translated (by Google) as both 'ever' and 'never'. When you form a question such as "Hai visitato Roma mai?" this would be "Have you ever visited Rome?" - the response can be 'Yes (I have visited Rome)' or ' No, never (I have never visited Rome). So effectively 'never' = non mai - it is the negative form combining the words 'no' + 'ever'