Learn Swedish: Vi hoppar över kapitel tre. - We are skipping chapter three.

Hoppar över is a particle verb (partikelverb), meaning the verb and the preposition work together to create a new meaning (literally "jump over"). In Swedish, you must put the spoken stress on the particle, which is över. The verb hoppar is left unstressed.

Why is it kapitel tre instead of tredje kapitlet?

Both ways work, just like in English. When you use the standard number as a label (tre), it comes after the noun in its indefinite form (kapitel tre for "chapter three"). If you use the ordinal number ("third"), it comes before the noun and requires the definite form (det tredje kapitlet for "the third chapter").

I've heard Swedish people use the word skippa. Could I use that in this sentence instead?

Absolutely. Skippa is a very common loanword from English and fits perfectly in everyday conversation: Vi skippar kapitel tre. Hoppar över is slightly more standard and works well in both casual and formal contexts.

The translation says "We are skipping", but hoppar is simple present tense. Why isn't there a continuous verb form here?

Swedish doesn't have a direct equivalent to the English "-ing" form (present continuous) to show that an action is happening right now. The simple present tense (hoppar) covers both "we skip" and "we are skipping". Swedish also frequently uses the present tense to express a decided future action.