Learn Hardcore German: Nach dem ersten Training hatte ich zwei Tage lang starken Muskelkater. - After the first training I had bad sore muscles for two days.

nach → dative
dem → definite article, dative singular (neuter)
After a definite article (dem / der / den etc.), adjectives take the weak declension, and in the dative singular for all genders the adjective ending is -en.

So:

dem ersten Training
dem kleinen Kind
der alten Frau
dem roten Auto

In each case: dative singular + definite article → adjective ends in -en.

Could I also say Ich hatte nach dem ersten Training zwei Tage lang starken Muskelkater? Why does the sentence start with Nach dem ersten Training?

Yes, both word orders are correct:

Nach dem ersten Training hatte ich zwei Tage lang starken Muskelkater.
Ich hatte nach dem ersten Training zwei Tage lang starken Muskelkater.

German is a verb-second (V2) language in main clauses:

The conjugated verb (here: hatte) must be in second position.
The first position can be different elements: subject, time phrase, place phrase, etc.

In your sentence, the time phrase Nach dem ersten Training is put first for emphasis or style. Then the verb hatte must come second, and ich moves after the verb.

Neutral, “unmarked” word order is often with the subject first:

Ich hatte nach dem ersten Training zwei Tage lang starken Muskelkater.

Starting with Nach dem ersten Training just highlights when it happened.

Why is it hatte and not habe gehabt or some form of the present perfect?

German has two common past tenses:

Präteritum (simple past)
- ich hatte = I had
Perfekt (present perfect)
- ich habe gehabt = I have had

Usage:

In spoken German, people usually prefer the Perfekt with most verbs:
- Ich habe zwei Tage lang starken Muskelkater gehabt.
In written German (especially narratives, stories, reports), the Präteritum is very common and sounds more natural:
- Nach dem ersten Training hatte ich zwei Tage lang starken Muskelkater.

So in a written example sentence, hatte is stylistically more typical.
In daily speech, many would say: Nach dem ersten Training habe ich zwei Tage lang starken Muskelkater gehabt.

What does zwei Tage lang mean exactly, and why do we use lang here?

Zwei Tage lang literally means for two days (in duration).

zwei Tage = two days (accusative plural)
lang here is an adverb that emphasizes the duration of time.

You can think of it as:

zwei Tage lang ≈ for a duration of two days

Without lang, zwei Tage can be understood, but it sounds less natural in this position:

Ich hatte zwei Tage lang starken Muskelkater. ✔︎ (very natural)
Ich hatte zwei Tage starken Muskelkater. ✔︎ (possible, but sounds a bit more clipped)

Lang is typical after a time expression to mark duration:

stundenlang = for hours
tagelang = for days
eine Woche lang = for a week

Why is it zwei Tage and not something with a preposition, like für zwei Tage?

Both are possible, but they’re not used in exactly the same way.

zwei Tage lang (or just zwei Tage in accusative) is the standard way to express actual duration:
- Ich hatte zwei Tage lang starken Muskelkater.
  = I had muscle soreness for two days (in fact).
für zwei Tage often suggests intended / planned duration, especially with verbs like mieten, buchen, kaufen:
- Ich miete das Auto für zwei Tage.
- Ich kaufe Essen für zwei Tage.

In your sentence, we’re talking about how long the soreness actually lasted, so zwei Tage lang (accusative of duration) is the most natural choice.
Ich hatte für zwei Tage starken Muskelkater is understandable but sounds unusual.

What case is zwei Tage in, and why is there no article?

Zwei Tage is in the accusative plural and it’s an example of the accusative of duration.

German often uses the accusative without a preposition to express how long something lasts:

Ich habe drei Stunden gearbeitet. – I worked for three hours.
Er blieb eine Woche. – He stayed for a week.
Wir warteten den ganzen Tag. – We waited (for) the whole day.

In your sentence:

zwei Tage (lang) = duration (for two days)
No article is needed because zwei already makes it specific: “two days”, not “the two days”.

Why is it starken Muskelkater and not starker Muskelkater?

This is about case and adjective endings.

The phrase starken Muskelkater is the direct object of hatte, so it must be in the accusative masculine singular:

Nominative: starker Muskelkater (e.g. Starker Muskelkater ist unangenehm.)
Accusative: starken Muskelkater (e.g. Ich hatte starken Muskelkater.)

Without an article, adjectives take the strong declension. For masculine:

Nominative: starker Muskelkater
Accusative: starken Muskelkater

Since ich hatte (I had) something (object), we need the accusative form → starken Muskelkater.

Could I also say einen starken Muskelkater instead of just starken Muskelkater?

Yes, both are grammatically correct:

Ich hatte starken Muskelkater.
Ich hatte einen starken Muskelkater.

The difference is subtle:

einen starken Muskelkater sounds a bit more concrete and specific, like “a really bad case of muscle soreness”.
starken Muskelkater is a bit more generic, like talking about muscle soreness as a state.

In everyday speech, many native speakers might naturally say:

Ich hatte einen starken Muskelkater.

Your original version without einen is also fully correct and common, especially in written or slightly more formal style.

Why do you say Muskelkater haben and not something like Ich bin Muskelkater?

In German, physical conditions like pain, illnesses, or states of the body are usually expressed with haben (to have), not sein (to be):

Ich habe Muskelkater. – I have sore muscles.
Ich habe Kopfschmerzen. – I have a headache.
Ich habe Fieber. – I have a fever.
Ich habe Hunger / Durst. – I am hungry / thirsty.

So the natural expression is Muskelkater haben, not Muskelkater sein.
Ich bin Muskelkater would mean “I am muscle soreness”, which doesn’t make sense.

What exactly does Muskelkater mean, and why is Kater (tomcat) in the word?

Muskelkater means muscle soreness or stiff / aching muscles after exercise.

Muskel = muscle
Kater normally = tomcat (male cat), but in another meaning it also refers to a hangover after drinking alcohol.

Historically, Kater in Muskelkater is not directly about cats; it comes from an older word related to catarrh (a kind of inflammation), and the word changed over time. But for a learner, it’s enough to know:

Muskelkater = the aches and soreness you feel in your muscles after intense physical activity.

Could I change the word order to Zwei Tage lang hatte ich nach dem ersten Training starken Muskelkater or Zwei Tage lang hatte ich starken Muskelkater nach dem ersten Training?

German word order is flexible, especially for time and other adverbials.

These are all grammatically correct, but differ in emphasis:

Nach dem ersten Training hatte ich zwei Tage lang starken Muskelkater.
– Focus first on when it was (after the first training).
Ich hatte nach dem ersten Training zwei Tage lang starken Muskelkater.
– Neutral, subject first.
Zwei Tage lang hatte ich nach dem ersten Training starken Muskelkater.
– Strong emphasis on the duration.
Zwei Tage lang hatte ich starken Muskelkater nach dem ersten Training.
– Grammatically OK but sounds slightly awkward; nach dem ersten Training fits more naturally earlier in the sentence.

Most natural choices in everyday language are (1) and (2).

Could I say Nach meinem ersten Training instead of Nach dem ersten Training? Is there a difference?

Yes, you can say:

Nach meinem ersten Training hatte ich zwei Tage lang starken Muskelkater.

Difference in nuance:

Nach dem ersten Training
– “After the first training” (could be understood more generally, e.g., the first session in a series, not necessarily your personal first ever).
Nach meinem ersten Training
– Emphasizes that this was your first training (e.g., the first time you ever trained, or your first session of that specific kind).

Grammatically:

mein is a possessive determiner, and with nach (dative), it becomes meinem:
- nach + meinem + ersten Training (dative singular neuter)
- Adjective still gets -en → ersten.