In probably all Indo-Germanic languages - at least in Spanish, French, Italian, Persian, English, German and Latin - the change of verbs follows a certain logic. It's hard enough to learn this logic and then there are exceptioins to this logic, which makes things not even easier.

Of the irregular verbs, there are two types. The first are the ones that change only their way of writing (not the way they are spoken). They are only in their spelling different to ensure the regularity of the spoken language. In the spoken language, they are not even irregulars. Let's have a look at an example.

vencer = to win
same logic:
convencer = to convince

indicativo
presente yo venzo tú vences él vence nosotros vencemos vosotros vencéis ellos vencen	imperfecto yo vencía tú vencías el vencía nosotros vencíamos vosotros vencíais ellos vencían	indefinido yo vencí tú venciste él venció nosotros vencimos vosotros vencisteis ellos vencieron	futuro venceré vencerás vencerá venceremos venceréis vencerán
subjuntivo
presente yo venza tú venzas él venza nosotros venzamos vosotros venzáis ellos venzan	imperfecto yo venciera tú vencieras él venciera nosotros venciéramos vosotros vencierais ellos vencieran	imperativo   vence (no venzas) venza Usted (no venza Usted) venzamos venced (no venzáis) venzan Ustedes	condicional yo vencería tú vencerías él vencería nosotros venceríamos vosotros venceríais ellos vencerían

with convencer: yo convenzo, tú convences... yo convencí, tú convenciste... yo convenza, tú convenzas... etc.

As you can see, vencer changes its stem in the first person singular in presente indicativo and in all the forms of the subjuntivo. This is only a different spelling to ensure the phonetical consistence. If not changed the the first person singular in presente indicativo would be:

venco = spoken: venko

Now it would be irregular because the sound of [c] would change to [k]. This is due to the rule that before the vocals a and o c is spoken k. These kinds of irregularities are derived irregularities.

Then there are the genuine irregular verbs that change not only in spelling but also in the way they are spoken. We will give an overview that include the imperfect, which actually has hardly any irregularities but it's easier to learn this way.

There are about 2,000 verbs, 1,000 of those have some kind of irregularity. But don't worry there aren't 1,000 different irregularities but only about 80. Most of them follow a certain scheme. Some verbs have more than one irregularity. One of those is colgar = to hang.

colgar = to hang

indicativo
presente yo cuelgo tú cuelgas él cuelga nosotros colgamos vosotros colgáis ellos cuelgan	imperfecto yo colgaba tú colgabas él colgaba nosotros colgábamos vosotros colgabais ellos colgaban	indefinido yo colgué tú colgaste él colgó nosotros colgamos vosotros colgasteis ellos colgaron	futuro yo colgaré tú colgarás él colgará nosotros colgaremos vosotros colgaréis ellos colgarán
subjuntivo
presente yo cuelgue tú cuelgues él cuelgue nosotros colguemos vosotros colguéis ellos cuelguen	imperfecto yo colgara tú colgaras él colgara nosotros colgaramos vosotros colgarais ellos colgaran	imperativo - cuelga (no cuelgues) cuelgue Usted (no cuelgue Usted) colguemos (no colguemos) colgad (no colguéis) cuelguen Ustedes (no cuelguen)	condicional yo colgaría tú colgarías él colgaría nosotros colgaríamos vosotros colgaríais ellos colgarían
gerundio: colgando participio perfecto: colgado

This verb shows two changes. The o turns an u, and after g is an u added (again because of the pronunciation rule that g is spoken with a throat-sound when it is before i or e). Therefore, it is tú cuelgues and not tú cuelges. In the following we have distinguished between genuine irregular verbs and derived irregular verbs. If a verb has two irregularities, a genuine one and a derived one, it is to be found among the genuine irregular verbs only.

We now will have a look first at the genuine irregular verbs and the first ones are so irregular that even the imperfect is irregular.