Learn German: Gestern hatte mein Kollege viel Stress. - Yesterday my colleague had a lot of stress.

hatte is the simple past tense of haben (to have). Because the sentence starts with Gestern (yesterday), we need the past tense to say the colleague 'had' stress, rather than 'has' (hat) stress.

Why does the verb hatte come before the subject mein Kollege?

In German, the main verb must be in the second position of a statement. Because the time word Gestern takes the first position, the verb hatte must come second. This pushes the subject (mein Kollege) into the third position. You cannot say 'Gestern mein Kollege hatte' like you would in English.

Why is it viel Stress and not viele Stress?

You use viel (much or a lot of) for things you cannot count, like Stress, time, or water. You use viele (many) for plural things you can count, like apples or cars.

Since Kollege is a masculine noun, why does it use mein instead of meinen?

mein Kollege is the subject of the sentence (he is the one who had stress), so it stays in the basic nominative case. You would only use meinen if the masculine noun was receiving the action as a direct object (the accusative case).