Im Kurs erklärt die Lehrerin die Präposition mit.

Im is a very common contraction of in dem.

So:

• in dem Kurs = im Kurs

German often contracts:

• in dem → im
• an dem → am
• zu dem → zum
• zu der → zur

In this sentence, im Kurs means in the course / in class.

Because this sentence describes a location, not movement.

German uses in with:

• dative for a static location: im Kurs
• accusative for movement into something: in den Kurs

So:

• Im Kurs erklärt die Lehrerin ... = she is already in the class/course, and that is where the action happens.
• Sie geht in den Kurs. = she goes into the class/course.

Here, no movement is involved, so dative is used.

Because German main clauses normally follow the verb-second rule.

That means the finite verb must be in the second position. In this sentence, Im Kurs is placed first for emphasis or topic, so the verb must come next:

• Im Kurs | erklärt | die Lehrerin | die Präposition mit

Even though die Lehrerin is the subject, it comes after the verb because Im Kurs has taken the first position.

Die Lehrerin is the subject because it is the person doing the action of explaining.

A few clues help:

1. erklärt is third-person singular, which matches die Lehrerin
2. Semantically, a teacher is the one who explains something
3. erklären normally takes a direct object, and here that object is die Präposition mit

So the structure is:

• die Lehrerin = subject
• die Präposition mit = direct object

It is the present tense, third-person singular form of erklären.

Conjugation:

• ich erkläre
• du erklärst
• er/sie/es erklärt
• wir erklären
• ihr erklärt
• sie/Sie erklären

Since die Lehrerin means the teacher and is singular, the correct form is erklärt.

Here die Präposition mit is the direct object of erklärt, so it is in the accusative case.

The noun Präposition is feminine:

• nominative: die Präposition
• accusative: die Präposition

For feminine nouns, the article die stays the same in both nominative and accusative, so the form does not change.

That is why you see die Präposition here.

No. Here mit is being mentioned as a word, not used in its normal grammatical function.

The phrase die Präposition mit means:

• the preposition mit

So mit is the word being explained.

If mit were being used as a real preposition in the sentence, it would normally have its own object, for example:

• mit dem Buch
• mit der Freundin

But in your sentence, the teacher is explaining the word mit itself.

Because it belongs to the noun phrase die Präposition mit.

That whole phrase means:

• the preposition mit

So mit is not floating freely at the end; it is attached to die Präposition as the specific preposition being named.

You can think of it as similar to English:

• The teacher explains the preposition with.

That may look a little unusual at first, but it is normal when you are talking about a word.

Because Präposition is a noun, and all German nouns are capitalized.

That is why you see:

• Kurs
• Lehrerin
• Präposition

Even grammar terms such as Verb, Nomen, Artikel, and Präposition are nouns, so they are capitalized.

Yes. German word order is flexible as long as the verb-second rule is respected in a main clause.

For example, you could also say:

• Die Lehrerin erklärt im Kurs die Präposition mit.

This is also correct. The difference is mostly one of focus:

• Im Kurs erklärt die Lehrerin ... puts in class / in the course first
• Die Lehrerin erklärt im Kurs ... puts the teacher first

Both are grammatical. The original sentence simply gives extra prominence to Im Kurs.