Learn Farsi: استاد خودش آن مقاله را می‌خواند. - The professor reads that article himself.

The base word خود means self. To emphasize who is doing the action, we attach the pronoun ending that matches the subject. Since the professor (استاد) is a third-person singular subject, we add the ending ش to make خودش (himself or herself).

Could we just leave خودش out of this sentence entirely?

Yes. If you just say استاد آن مقاله را می‌خواند, it simply means the professor reads that article. Placing خودش right after the subject adds the emphatic himself, showing that the professor personally reads it instead of having an assistant do it.

Does خودش change if the professor is a woman?

No, because Farsi pronouns and endings do not have gender. The word استاد can refer to a male or female professor, and خودش translates to either himself or herself depending entirely on who you are talking about in context.

Why do we need the word را after آن مقاله?

The word را marks a specific direct object. Because the professor is reading a very specific article, which is pointed out by the word آن (that), we must put را immediately after آن مقاله to show it is the specific thing receiving the action of the verb.