Learn Hardcore Korean: naenyeone gyeongjehak sueobeul deureoyo. - I will take an economics course next year.

내년 means “next year,” and -에 is a time marker that translates to “in” or “at” when attached to years, months, days, times, etc. So 내년에 = “in/at next year,” indicating when the action happens.

The verb is 들어요 (“to listen”). How does it mean “to take” a class here?

Literally, 듣다 means “to listen.” But 수업을 듣다 is an idiomatic expression meaning “to attend” or “to take” a lesson/class—as if you “listen to” the instruction.

Why is the simple present tense 들어요 used for a future event (“next year”)? Isn’t that the future tense?

Korean often uses the plain present tense for scheduled or planned future events, similar to English “The train leaves tomorrow.” If you want to emphasize the future, you can use -ㄹ 거예요:
내년에 경제학 수업을 들을 거예요.

What does 경제학 mean, and why the suffix -학?

경제 means “economy,” and -학 is a suffix meaning “study of” or “science.” Together, 경제학 means “economics” (the academic field).

There’s no subject like 저는 or 내가. Why is it omitted?

Korean often drops the subject when it’s understood from context. Here, “I” is implied, especially since the verb ends in -요 (polite speech). You could add 저는 for clarity:
저는 내년에 경제학 수업을 들어요.

Why is the object marker -을 attached to 수업 instead of -를?

Object markers -을/를 depend on the final sound of the noun:
• Use -을 after a consonant (수업 ends with ㅂ, a consonant).
• Use -를 after a vowel.

Can I replace 수업을 듣다 with 수강하다?

Yes. 수강하다 means “to enroll in” or “to attend a course” in a more formal/registerd style. You could say:
내년에 경제학을 수강해요.
But 수업을 듣다 is more common in everyday conversation.

What’s the difference between 수업을 듣다 and 수업을 받다?

While both can convey “taking a class,” 수업을 듣다 (“to listen to a class”) is the standard idiom for “attend a class.” 수업을 받다 (“to receive a class”) is less idiomatic and rarely used.

If I want to add a location (like “at university”), how would I do that?

Add 에서 after the location noun:
내년에 대학교에서 경제학 수업을 들어요.
Here, 대학교에서 means “at the university.” You can drop it if the venue is obvious.