Учитель вводит новую тему грамматики.

Because новую has to match тему, and тему is the direct object of the verb.

• Dictionary form: новая тема = a new topic
• In this sentence: новую тему = accusative singular feminine

So:

• новая тема = subject form
• новую тему = object form

Russian adjectives must agree with the noun in gender, number, and case.

For the same reason: тема is the direct object of вводит, so it goes into the accusative case.

• Dictionary form: тема
• Accusative singular: тему

Since вводить is a transitive verb, it normally takes a direct object in the accusative.

Because тема often takes another noun in the genitive to show what the topic is about.

So:

• тема грамматики = a topic of grammar / a grammar topic
• урок истории = a history lesson
• правило произношения = a pronunciation rule

Here грамматики is genitive singular, meaning of grammar. English often translates this more naturally as grammar topic or topic in grammar.

Here вводит means introduces or brings in.

The verb вводить literally has the idea of leading/bringing something in, but in teaching it is commonly used for introducing new material, a new topic, a new concept, and so on.

So Учитель вводит новую тему грамматики means something like:

• The teacher introduces a new grammar topic
• The teacher is introducing a new grammar topic

Yes. Вводит is present tense, 3rd person singular, from the imperfective verb вводить.

In Russian, the present tense of an imperfective verb can mean:

• a general or habitual action: The teacher introduces
• an action happening now: The teacher is introducing

Context tells you which one is meant.

If you wanted a future completed action from the perfective verb, you would use введёт:

• Учитель введёт новую тему грамматики = The teacher will introduce a new grammar topic

Here is the breakdown:

• Учитель — nominative singular; the subject
• вводит — verb, 3rd person singular present
• новую — accusative singular feminine; agrees with тему
• тему — accusative singular feminine; direct object
• грамматики — genitive singular; depends on тема

So the basic structure is:

subject + verb + direct object + dependent genitive noun

Because Russian has no articles.

English has a and the, but Russian usually leaves that idea to context. So Учитель can mean:

• the teacher
• a teacher

And новую тему can mean:

• a new topic
• the new topic

The exact English translation depends on the situation.

Yes. Russian word order is more flexible than English because the case endings show each word’s role.

The neutral word order here is:

• Учитель вводит новую тему грамматики.

But you could also say:

• Новую тему грамматики вводит учитель.
• Учитель новую тему грамматики вводит.

These versions would sound more marked and would shift the emphasis, but the basic meaning stays the same because the endings still show who is doing what.

Possibly, but the noun учитель is grammatically masculine.

A few useful points:

• учитель is the standard dictionary form
• учительница is a common word for a female teacher
• in some contexts, учитель can be used more generally or officially

In this sentence, the verb вводит does not show gender, so gender is only suggested by the noun itself. If you specifically wanted female teacher, учительница would usually make that clearer.

Yes, both are possible, but they are slightly different in feel.

• новую тему грамматики = a new topic of grammar
• новую тему по грамматике = a new topic in grammar; this is very common in classroom language
• новую грамматическую тему = a new grammatical topic

All are understandable. In many teaching contexts, тему по грамматике may sound especially natural, while тема грамматики is still perfectly clear.

Because of the case endings.

• Учитель is in the nominative case, which is the normal case for the subject.
• тему is in the accusative case, which marks the direct object.

So even if the word order changed, the endings would still tell you that the teacher is doing the action and the topic is being introduced.