Learn Hardcore Korean: jaknyeone hangugeoreul bae-ugi sijakhaesseoyo.

작년 means “last year” in Korean. The particle -에 is a time marker that attaches to nouns to indicate “at,” “on,” or “in” a point in time. So 작년 + -에 = 작년에, which translates as “last year” or “in last year.”

Why is -를 used in 한국어를 instead of -을?

Korean has two object markers: -을 (after consonants) and -를 (after vowels). Since 한국어 ends in the vowel ㅓ, you use -를 to mark it as the direct object of the verb. Thus 한국어를 means “Korean (language)” as the thing being learned.

How does 배우기 시작했어요 break down grammatically?

This phrase is made of three parts:

배우다 (to learn) – the base verb.
-기 – a nominalizer that turns the verb into a noun-like form (배우기, “learning”).
시작하다 (to begin/start) – in the past polite form 시작했어요, “started.”

So 배우기 시작했어요 literally means “(I) started learning.”

Why is there -었 in 시작했어요? What tense and politeness level is that?

-었- (or -았-/었-) is the past-tense marker.
시작했- is the stem of 시작하다 in past form.
-어요 is the polite (informal polite) sentence ending used in everyday conversation.

Altogether, 시작했어요 is the polite past tense, “(I) started.”

Why does the time expression 작년에 come at the beginning of the sentence?

Korean generally follows a Time–Topic–Subject–Object–Verb order. Time adverbs (like 작년에) often appear first to set the temporal context, whereas in English we can be more flexible. Placing 작년에 at the front emphasizes “last year” as the time frame.

Is it necessary to include the subject “I” in this sentence? Why is there no 저는 or 제가?

In Korean, subjects and topics are often omitted when they’re clear from context. Since you’re likely talking about yourself, you can drop 저는 (“as for me”) or 제가 (“I” as subject) without causing confusion. The verb ending -어요 already implies the first-person subject in this context.

Could you rephrase 작년에 한국어를 배우기 시작했어요 in a more casual form?

Sure. In casual speech you could say:

지난해 한국어 배우기 시작했어.
Here, 지난해 is another way to say “last year,” you drop the object particle -를 (한국어 배우기), and you change the ending to -었어 for casual past.