Learn Swedish: Jag såg att du inte började på nästa kapitel. - I saw that you did not start on the next chapter.

In Swedish, the word nästa (next) is a bit special. Unlike most words that point to a specific thing, nästa requires the noun that follows it to be in the indefinite form (without the "the" ending). So we say nästa kapitel (next chapter) rather than nästa kapitlet.

Why does inte come before the verb började here?

This sentence follows a very important rule for subordinate clauses (a part of a sentence that starts with a linking word like att, meaning "that"). In these clauses, words like inte (not) or alltid (always) must be placed before the verb. Since att du inte började... is a subordinate clause, inte is placed in front of började.

Why do we use the preposition på after the verb?

You use börja på when you mean "start working on" or "start reading" a specific task, like a chapter or a project. If you were just saying "the chapter started", you would drop på and simply say kapitlet började.

What form of the verb is såg?