Learn Swedish: Jag bryr mig inte om priset. - I do not care about the price.

In Swedish, the verb for 'to care' is reflexive: att bry sig. You always need a reflexive pronoun that matches the subject. So, you literally say 'I care myself' (jag bryr mig). For other subjects, it changes: han bryr sig (he cares), vi bryr oss (we care).

Why is inte placed after mig?

In a standard Swedish sentence, the word inte (not) usually goes right after the verb. However, if there is a pronoun object like mig, that pronoun hugs the verb closely, pushing inte to the next spot: Verb + Pronoun + inte.

Does om mean 'about' here? I thought it meant 'if'.

It means both! As a connecting word between sentences, om means 'if'. But as a preposition, it often means 'about'. The combination att bry sig om is a fixed phrase meaning 'to care about'.

What is the base word for priset?

The base word is pris (price). Because it is an 'ett'-word (ett pris), it takes the -et ending to become the definite form. Therefore, priset translates to 'the price'.