In fact, there are 3 categories of verbs:
1) Weak Verbs
2) Strong Verbs
3) Irregular Verbs
1) An English weak verb forms its past tense and past participle forms simply by adding the suffix "-(e)d" to the stem:
examples:
to live - pt: lived - pp: lived
to wish - pt: wished - pp: wished
2) Strong verbs in comparison change their stem vowel in the past tense and have either no added suffix, or take the old -en ending in the past participle:
examples:
to sing - pt: sang - pp: sung
to write - pt: wrote - pp: written
to take - pt: took - pp: taken
--> It is said very often, that strong verbs are irregular verbs, but that's not true. Strong verbs form their forms in a different way than weak verbs, but this happens after a regular paradigm, e.g.:
write - wrote - written
goes like ride - rode - ridden
and like rise - rose - risen
and sing - sang - sung
goes like sink - sank - sunk... and so on.
Most of all the verbs can be put in one of these 2 large groups.
3) A hand full of verbs can be regarded to be irregular. These verbs cannot be put in one of the 2 groups mentioned above because they form their past tense and past participle forms in an irregular way.
Verbs belonging to this group are e.g.
to be - was/were - been
to go - went - gone
to do - did - done
to bring - brought - brought
to catch - caught - caught
to make - made - made
and the Modal helping verbs
can, may, must, shall, will.
-> These verbs are very irregular and also defective because they don't have an infinitive, past participle form and no real past tense form.
can, may and must need to be paraphrased by other words to express the past tense:
can = to be able to
may = to be allowed to
must = to have to
Hope this helps