Modals or modal verbs are a kind of verbs which are always connected to change in mood. However, mood here covers more things than just 'atmosphere'. Modality indicates all the feelings a person can experience towards an object in a sentence - will, intention, possibility, obligation, etc.
Modals themselves do not have any forms! They do not take either infinitive or participle form, also, they don't take -(e)s in the third person singular.
We might say that modals have only two forms, basic, present and preterite (which not always has to be past!). That is why we have pairs of modals in English, like:
Can <---> Could
May <---> Might
Shall <---> Should
Will <---> Would