One should be aware that there are three different types of irregular verbs. What we are going to say now is valid as well for Spanish and French.
1) irregular in writing, but not in the pronunciation
In this grammar we don't call a verb that suffers a modification of its radical in writing, but not in the pronunciation irregular because that would be really strange. A verb which suffers a modification of its radical just to maintain the regularity of the pronunciation is not irregular because the important thing is how it is pronounced and not how it is written. Let's have a look at the verb cercare. It has in the present two irregularities.
lui / lei cerca
But is it useful or logical to say that cercare is a irregular verb? If we would write in a regular way as shown it below, it would be regular in writing, but very irregular in the pronunciation.
"regular" in writing
very irregular in the pronouciation
Because the c is pronounced like /k/ in front of a / o / u and pronounced like /tsch/ after i / e the pronunciation would change completely and so the h is necessary to preserve the pronunciation. Those who call this kind of verbs irregular suppose that the writing is more important than the pronunciation.
2) some forms are irregular in the pronounciation
If there is a change in the pronunciation of the radical of a verb we can really call it irregular. Irregular for example is the passato remoto of the verb dire in the first and third person singular as well as in the third person plural.
lui / lei disse
3) The verb is completely irregular
Some verbs are completely irregular, there is nothing left from the radical. This few words you have to learn by heart. It is a strange kind of phenomenon that in every language the most used verbs are the most irregular verbs. In any language for instance the very important verb to be is completely irregular.
to be (English)
he / she was
er / sie war
lui / lei era
él / ella era
ellos / ellas eran
This very frequent verbs we have already used in this manual several hundred times. Very few verbs are completely irregular and we know them all already.