Stack data structure implementation in Java
I'd like to give some thoughts which spring to my mind when I read your given code. Now, you have an implementation specific for primitive ints. A more advanced step would of course be to implement a generic Stack like the one in the JDK, just mentioning it. 

First up, I like that you use clear variable names, and that you reuse methods like isEmtpy \ isFull. Kudos for that! As an aside, you do not need the maxSize variable, as it is the same as stack.length.

It is a fixed size stack, so it does mean you have to know beforehand how much elements it would take up, in order to not waste space (or run out of it). Perhaps for a follow up exercise you could try and make it dynamically resizable?

Now, for the push method. I would not let it silently succeed if the stack is already full. Seeing as it is a fixed size stack, I would probably opt to throw an Exception, because to me it looks like a programming error. A possible second idea could be to return a boolean, signaling succes or failure (though I don't think it is the better solution).

Same with peek. It now silently succeeds and returns 0, which is very well a valid value which could reside in the stack (EmptyStackException exists by the way!). The boolean solution would not work here of course. Also, I personally do not think the extra new line is an improvement, on the contrary.

Finally, to me pop means taking off the top element of the stack. So why not return it?