Learn Hardcore German: Nach dem Unterricht gehe ich in die Stadt.

The preposition nach (in the sense of after) always takes the dative case.
Unterricht (lesson / class / instruction) is masculine:
- Nominative: der Unterricht
- Accusative: den Unterricht
- Dative: dem Unterricht

Since nach requires dative, you must use dem Unterricht:
nach + dem Unterricht → nach dem Unterricht (“after class / after the lesson”).

You would never say nach den Unterricht or nach der Unterricht here; those forms are simply wrong for this noun and this preposition.

Does nach always mean “after”?

No. nach has two very common meanings:

“after” (time) – always with dative
- Nach dem Unterricht gehe ich in die Stadt. = After class I go into town.
- Nach dem Essen = after the meal
“to” (direction, mostly with cities, countries, cardinal directions) – also with dative
- Ich fahre nach Berlin. = I’m going to Berlin.
- Wir fliegen nach Deutschland. = We’re flying to Germany.
- Nach Norden = to the north

So the preposition is the same, but the meaning depends on context. In your sentence, the temporal meaning “after” is used.

Why does the sentence start with Nach dem Unterricht instead of Ich?

German word order is quite flexible, but the finite verb must be in second position in main clauses (the V2 rule).

You can put a time phrase at the beginning for emphasis or for a natural flow:

Nach dem Unterricht gehe ich in die Stadt.
- First element: Nach dem Unterricht (a time expression)
- Second element (the verb): gehe
- Then the subject: ich

You could also say:

Ich gehe nach dem Unterricht in die Stadt.

Both are correct and mean the same. Starting with Nach dem Unterricht just emphasizes when you go to town: “After class, I go into town.”

Is Ich gehe nach dem Unterricht in die Stadt also correct? Is there any difference?

Yes, it is completely correct:

Nach dem Unterricht gehe ich in die Stadt.
Ich gehe nach dem Unterricht in die Stadt.

Both are grammatical and mean the same in everyday use.

Differences:

First version: Emphasis a bit more on “after class” (time comes first).
Second version: Starts with the subject ich, which is more neutral.

In practice, both are very natural, and the difference is subtle.

Why is it gehe ich instead of ich gehe after Nach dem Unterricht?

Again, this is the verb-second rule:

The first slot in the sentence is taken by Nach dem Unterricht (a whole phrase).
The finite verb must still be in second position, so it comes right after that: gehe.
The subject ich then follows the verb.

So the structure is:

Nach dem Unterricht (1st position)
gehe (2nd position = verb)
ich (rest of the clause)
in die Stadt (rest)

That’s why the order becomes Nach dem Unterricht gehe ich …, not Nach dem Unterricht ich gehe …, which would be wrong in standard German.

Why is it in die Stadt and not in der Stadt?

Because in can take either accusative or dative, depending on the meaning:

Accusative (Wohin? – where to?) → motion towards a place
Dative (Wo? – where?) → location, being at/in a place

In your sentence:

in die Stadt uses the accusative (die Stadt) because you are going to the city (movement towards).
in der Stadt would be dative, and would mean “in the city” (location, already there).

Compare:

Ich gehe in die Stadt. = I’m going into town. (movement → accusative)
Ich bin in der Stadt. = I’m in town. (location → dative)

Why is it die Stadt? What gender and case is Stadt here?

Stadt (city, town) is a feminine noun:

Nominative singular: die Stadt
Accusative singular: die Stadt (same form as nominative for feminine nouns)
Dative singular: der Stadt

In in die Stadt:

The preposition in with movement (going into) needs the accusative.
Feminine accusative singular is die.

So you get in die Stadt.

If it were location (no movement), it would be dative:

in der Stadt = in the city (no movement, just location)

Why is Stadt capitalized? And why is Unterricht capitalized?

In German, all nouns are capitalized, regardless of their position in the sentence.

die Stadt → Stadt is a noun → capital letter
der Unterricht → Unterricht is also a noun → capital letter

This is a fixed rule in German spelling: every noun (and certain words used as nouns) starts with a capital letter, even in the middle of a sentence.

Why is the verb gehe used here? Could I also use fahre?

Both can be possible, but they mean slightly different things:

gehen = to go on foot, to walk
- Ich gehe in die Stadt. → I’m going into town on foot.
fahren = to go / drive using a vehicle (car, bus, train, bike, etc.)
- Ich fahre in die Stadt. → I’m going into town by some means of transport.

In everyday speech, people often use gehen even if they might not literally walk the entire way, but the strict distinction is:

gehen: walking
fahren: traveling by vehicle

Why is the present tense gehe used instead of a future form like werde gehen?

German uses the present tense very often for future actions, especially when the context already shows it’s about the future:

Nach dem Unterricht gehe ich in die Stadt.
→ “After class I’ll go into town.”

Using the future tense:

Nach dem Unterricht werde ich in die Stadt gehen.

is grammatically correct, but in many everyday contexts it sounds more formal or more emphatic than necessary. The simple present is usually preferred if the time is clear from context (like nach dem Unterricht).

What exactly does Unterricht mean here? Is it the same as Schule or Klasse?

Not exactly the same:

Unterricht = instruction / teaching / (a period of) lessons
- Refers to the teaching activity or class time itself.
- Nach dem Unterricht = after the lesson(s) / after class.
Schule = school (the institution or the building, or school in general)
- Nach der Schule can mean after school is over (for the day or overall).
Klasse = class in the sense of a group of students or sometimes a lesson, depending on region.
- Nach der Klasse is not as standard in German for “after class”; nach dem Unterricht or nach der Stunde is more typical.

So Nach dem Unterricht emphasizes after the teaching period rather than after the entire school day as a whole.

Can in die Stadt gehen also mean “go downtown” rather than just “go to the city”?

Yes. In many contexts, in die Stadt gehen is best translated as “go into town” or “go downtown”, not usually “go to the (big) city” in a geographical sense.

It often implies:

going to the city center / main shopping area
running errands, shopping, meeting friends, etc.

So contextually, “After class I’m going into town” is usually the most natural English rendering.