Na lekcji nowy temat wydawał mi się trudny, ale nauczyciel podał prosty przykład.

Na lekcji means in class, during the lesson, or literally at the lesson.

Polish often uses na with events, activities, and organized situations, for example:

• na lekcji — in class
• na spotkaniu — at a meeting
• na koncercie — at a concert

So na lekcji is the normal expression.

You would not usually say w lekcji here. If you wanted to stress the time meaning, you could say w czasie lekcji = during the lesson, but na lekcji is much more natural in everyday Polish.

Because the verb in the past tense agrees with the subject, which is nowy temat.

• temat is masculine singular
• so the past tense form is wydawał

Compare:

• temat wydawał się trudny — the topic seemed difficult
• lekcja wydawała się trudna — the lesson seemed difficult
• zadanie wydawało się trudne — the task seemed difficult

So the ending tells you the gender and number of the subject in the past tense.

Wydawać się means to seem or to appear.

In this sentence:

• nowy temat = the thing that seems difficult
• mi = to me
• się = part of the verb wydawać się
• trudny = difficult

So the structure is basically:

[something] wydaje / wydawał się [komuś] [jaki?]

Example:

• Temat wydawał mi się trudny. — The topic seemed difficult to me.

A very literal breakdown would be:

• nowy temat — the new topic
• wydawał się — seemed
• mi — to me
• trudny — difficult

So mi is not optional if you want to say to me, and się belongs with the verb.

Both forms can relate to I / me, but here mi is the normal unstressed dative form.

• mi = short, common, unstressed form
• mnie = longer, stressed or emphatic form

In this sentence, there is no special emphasis, so mi is the natural choice:

• wydawał mi się trudny

If you used mnie, it would sound more contrastive or emphatic, for example:

• Mnie wydawał się trudny, ale innym nie. — It seemed difficult to me, but not to others.

So for ordinary neutral speech, mi is best.

Because trudny is an adjective describing the subject temat, and with wydawać się an adjective like this is normally in the nominative, agreeing with the subject.

• temat — masculine singular
• so the adjective is trudny

That is why we get:

• temat wydawał się trudny

A useful comparison:

• On jest zmęczony. — He is tired.
• Temat wydawał się trudny. — The topic seemed difficult.

However, when the complement is a noun phrase, Polish often uses the instrumental:

• To wydawało mi się dobrym pomysłem. — It seemed like a good idea to me.

So:

• adjective alone: often nominative
• noun phrase: often instrumental

Here podał means gave or provided.

The verb podać has several related meanings depending on context, such as:

• to hand
• to serve
• to give
• to provide
• to state

In a school or explanation context, podać przykład is a very common phrase meaning:

• to give an example
• to provide an example

So:

• nauczyciel podał prosty przykład = the teacher gave a simple example

It is in the accusative, because it is the direct object of podał.

The teacher gave what?

• prosty przykład

But for masculine inanimate nouns in the singular, the accusative is the same as the nominative.

So:

• nominative: prosty przykład
• accusative: prosty przykład

That is why the form does not visibly change.

Compare that with a masculine animate noun, where the accusative does change:

• nominative: dobry nauczyciel
• accusative: dobrego nauczyciela

So przykład stays the same because it is masculine singular and inanimate.

This is about aspect.

• wydawał się is imperfective
• podał is perfective

They are used differently because they describe different kinds of actions.

Wydawał się describes a state or impression:

• the topic seemed difficult
• this is not a single completed action, but an ongoing impression

Podał describes a completed event:

• the teacher gave an example
• this happened as one finished action

So the sentence naturally combines:

• an ongoing impression: wydawał mi się trudny
• a completed action: nauczyciel podał prosty przykład

This is very typical in Polish.

The word order is somewhat flexible, but wydawał mi się is the most natural order here.

Polish short pronouns such as mi and się tend to stay close to the verb and usually do not go in strongly stressed positions.

So this is natural:

• Nowy temat wydawał mi się trudny.

This is also possible:

• Na lekcji nowy temat wydawał mi się trudny.

But something like:

• wydawał się mi trudny

is much less natural in ordinary speech.

So the sentence you have is a very normal Polish word order.

Because Polish does not have articles like English a/an and the.

So:

• nowy temat can mean a new topic or the new topic
• prosty przykład can mean a simple example or the simple example

The exact meaning comes from context, not from an article.

In this sentence, the context tells us that:

• nowy temat is the topic being discussed in class
• prosty przykład is an example the teacher gave

This is normal in Polish, and learners have to get used to relying more on context than on articles.