First of all remember a modal is a verb used to say something in a determinate way (modal is Spanish means modo de decir as well). Then you should pay attention to the grammar characteristic: is it an auxiliary or not?. This means that not all the modals are auxiliaries:
- You don't have to wear a uniform at work but you can't wear tra CAN iners
As you can see HAVE TO needs an axiliary for the negative form whiledoesn't need it because it's itself an auxiliary. If you want to know more about their characteristics you can go to this link.
To finish with, keep in mind there are few of them which use infinitive with TO: HAVE TO, OUGHT TO and USED TO; the rest use bare infinitive, that is, without TO.
Here you are some links about grammar to help you with MODALS:
- this is a list of modals and their use: click here
- this is another list: