Sau khi đi chợ, tôi sẽ nấu ăn trong bếp.

Sau khi means after in the sense of after doing something.

• sau = after / behind
• khi = when

Together, sau khi + verb phrase introduces an action that happens first:

• Sau khi đi chợ = After going to the market
• Sau khi ăn = After eating
• Sau khi học xong = After finishing studying

In your sentence, Sau khi đi chợ sets up the earlier action, and the main clause tells what happens next.

Vietnamese often omits the subject when it is obvious from context.

So:

• Sau khi đi chợ, tôi sẽ nấu ăn trong bếp.

is naturally understood as:

• After I go to the market, I will cook in the kitchen.

You can say sau khi tôi đi chợ, but it is often unnecessary unless you want to be extra clear or contrast subjects.

Compare:

• Sau khi đi chợ, tôi sẽ nấu ăn.
  = After going to the market, I will cook.

• Sau khi mẹ tôi đi chợ, tôi sẽ nấu ăn.
  = After my mother goes to the market, I will cook.

In the second example, the subject must be stated because it is not the same person.

It often means more than just physically going to a market building. In everyday Vietnamese, đi chợ commonly means:

• going to the market
• going grocery shopping
• going out to buy food and household items

So depending on context, đi chợ may be closer to go grocery shopping than to a literal go to the market.

That is why this sentence sounds very natural in Vietnamese daily life.

Sẽ is a future marker. It often means will.

• tôi sẽ nấu ăn = I will cook

Vietnamese verbs do not change form for tense the way English verbs do. Instead, words like sẽ help show time.

Common time-related markers include:

• đã = past
• đang = ongoing / progressive
• sẽ = future

Examples:

• Tôi nấu ăn. = I cook / I am cooking / I will cook, depending on context
• Tôi đang nấu ăn. = I am cooking
• Tôi sẽ nấu ăn. = I will cook

So yes, sẽ marks future meaning here.

You could say it, but without sẽ, the sentence is less clearly future.

• Sau khi đi chợ, tôi sẽ nấu ăn trong bếp.
  Clearly means: After going to the market, I will cook in the kitchen.

• Sau khi đi chợ, tôi nấu ăn trong bếp.
  Could sound like a habitual action, a narration, or a context-dependent statement.

Because English often requires a clear future form, learners usually find sẽ helpful. In natural Vietnamese, though, time can also be understood from context without it.

Nấu ăn is a very common expression meaning to cook.

• nấu = cook / boil / prepare by cooking
• ăn = eat

Together, nấu ăn means cook food / do cooking.

You may also hear just nấu, but nấu ăn is very common because it clearly refers to the activity of cooking.

Examples:

• Tôi đang nấu ăn. = I am cooking.
• Mẹ tôi nấu rất ngon. = My mother cooks very well.

So in this sentence, nấu ăn is completely natural.

Trong bếp means in the kitchen.

• trong = in / inside
• bếp = kitchen

So:

• trong bếp = inside the kitchen

Vietnamese often uses location words very directly. Here, trong emphasizes being physically inside that space.

You might also hear ở bếp, which means something like at/in the kitchen, but trong bếp specifically means inside the kitchen and works very well here.

Vietnamese word order in this sentence is very normal:

• Sau khi đi chợ = time clause first
• tôi = subject
• sẽ nấu ăn = future + verb phrase
• trong bếp = location

So the structure is:

After doing X, subject will do Y in location Z.

This is actually quite similar to English:

• After going to the market, I will cook in the kitchen.

Vietnamese often places time expressions near the beginning of the sentence, but English can do this too.

The comma is standard and helpful, especially in writing, because Sau khi đi chợ is an introductory time clause.

• Sau khi đi chợ, tôi sẽ nấu ăn trong bếp.

Without the comma, the sentence is still understandable:

• Sau khi đi chợ tôi sẽ nấu ăn trong bếp.

But the comma makes it easier to read and matches normal written punctuation.

Vietnamese does not use articles like a, an, and the the way English does.

So:

• chợ can mean market or the market
• bếp can mean kitchen or the kitchen

The exact meaning comes from context.

In this sentence:

• đi chợ naturally means go to the market / go grocery shopping
• trong bếp naturally means in the kitchen

This lack of articles is very normal in Vietnamese.

Sometimes yes, but it depends on context.

• Sau khi đi chợ, tôi sẽ nấu ăn trong bếp.
  Clear and complete.

In conversation, if it is already obvious who is speaking about themselves, a native speaker might omit tôi:

• Sau khi đi chợ, sẽ nấu ăn trong bếp.

However, this sounds less complete in isolation. For learners, it is safer and more natural to keep tôi unless the context clearly allows omission.

Yes, it is natural and correct.

A native speaker might also say similar things depending on context:

• Sau khi đi chợ, tôi sẽ nấu cơm.
  = After going to the market, I’ll cook.
  (Often nấu cơm can mean preparing a meal, not just cooking rice.)

• Đi chợ xong, tôi sẽ nấu ăn trong bếp.
  = After finishing the market trip, I’ll cook in the kitchen.

• Sau khi đi chợ về, tôi sẽ nấu ăn.
  = After coming back from the market, I’ll cook.

So your sentence is good, but Vietnamese has several natural ways to express the same idea.

Both can mean after going to the market, but they feel slightly different.

• Sau khi đi chợ = after going to the market
  More neutral, more textbook-friendly, very clear.

• Đi chợ xong = after finishing the market trip / once I’m done shopping
  More conversational and common in speech.

Examples:

• Sau khi đi chợ, tôi sẽ nấu ăn.
• Đi chợ xong, tôi sẽ nấu ăn.

Both are natural. Learners often start with sau khi, then later get used to patterns with xong.

Bếp can refer to:

• the kitchen
• the cooking area
• the stove, depending on context

In this sentence, trong bếp clearly means in the kitchen.

Context decides the exact meaning. For example:

• Tôi đang ở trong bếp. = I’m in the kitchen.
• Bếp ga này cũ rồi. = This gas stove is old.

So bếp is a flexible word, but here it definitely refers to the kitchen space.