to wonder
The phrase 'sich wundern' is used in German to express the act of wondering or being curious about something. It is a reflexive verb, meaning it requires a reflexive pronoun (such as 'sich') to be used correctly. For example, 'Ich wundere mich, warum das so ist' translates to 'I wonder why that is so'.
He will be surprised when he hears the news.
This sentence showcases the use of 'sich wundern' within a conditional clause. The verb 'wundern' is reflexive which means it always comes along with a reflexive pronoun (in third person, 'sich'). The subject 'er (he)' is getting the action of the verb, hence making him surprised (wondering) about some news he will hear in the future.
They should wonder why they were not invited.
In this example, the use of 'sich wundern' is suggestive. The speaker is urging the 'sie (they)' to question or to be surprised about the reasons why they were not invited. It shows the usage of 'sich wundern' in a context where it means 'to question' or 'to ponder'.
I would be surprised if that works.
Here, 'sich wundern' is used to express skepticism or doubt about a possible future event or situation. The speaker is implying that the success of whatever is being referred to (das) seems unlikely, thus they would be surprised (wundern) if it actually succeeds (klappt).