Obwohl ich gestern müde war, habe ich meine Notizen noch einmal gelesen, damit ich heute im Kurs sicherer bin.

Because obwohl is a subordinating conjunction. In German, a subordinate clause usually sends the conjugated verb to the end.

So:

• ich war müde = main clause word order
• obwohl ich müde war = subordinate clause word order

That is why war comes last in that clause.

Because the sentence begins with a subordinate clause: Obwohl ich gestern müde war.
When a subordinate clause comes first, the main clause still follows the normal German rule that the conjugated verb must be in position 2.

So the structure is:

• Obwohl ich gestern müde war,
• habe ich meine Notizen noch einmal gelesen

The whole first clause counts as position 1, so the verb habe must come immediately after it.

This is often called inversion.

Habe gelesen is the Perfekt tense, and in everyday spoken German this is very common for talking about the past.

So:

• ich las = simple past / literary or more formal in many contexts
• ich habe gelesen = very common in normal speech

A native speaker could say either, but ich habe gelesen sounds more natural in everyday conversation.

Noch einmal means again or one more time.

In this sentence, it suggests the speaker read the notes once more. It often has a slightly more literal sense of another time / one additional time than just wieder, although in many contexts they overlap.

So here:

• noch einmal gelesen = read again / read one more time

Meine Notizen is the direct object of gelesen because it is the thing being read.

The verb lesen takes an accusative object:

• ich lese die Notizen
• ich habe meine Notizen gelesen

Here, Notizen is plural, and meine is the matching possessive determiner in the accusative plural form.

Because müde is being used as a predicate adjective, not directly before a noun.

Compare:

• ich bin müde → predicate adjective, no ending
• der müde Student → adjective before a noun, with ending

In the sentence, müde goes with war:

• ich war müde = I was tired

So no adjective ending is needed.

Damit introduces a purpose clause: it explains why the speaker did something.

Here:

• ..., damit ich heute im Kurs sicherer bin
• ..., so that I am more confident today in class

German often uses um ... zu when the subject is the same in both parts:

• Ich lese meine Notizen noch einmal, um sicherer zu sein.

But damit is also very common, and it gives you a full clause with its own subject and verb:

• damit ich ... bin

So this sentence uses a very clear full purpose clause.

For the same reason as with obwohl: damit is also a subordinating conjunction.

That means the clause follows subordinate-clause word order, with the conjugated verb at the end:

• damit ich heute im Kurs sicherer bin

So both obwohl and damit trigger verb-final word order.

Yes. Sicherer is the comparative of sicher.

Here it means something like:

• more confident
• more sure
• less uncertain

German often uses the comparative even when the second comparison point is only implied. The idea is:

• more confident than before
• more confident than I would otherwise be

Also, because sicherer is a predicate adjective after bin, it does not take an ending.

Im is just the common contraction of in dem.

So:

• im = in dem

German very often uses these contractions in normal speech and writing.

Here:

• heute im Kurs = today in class / in the course

Both im Kurs and in dem Kurs are grammatically possible, but im Kurs is much more natural here.

This follows a very common German tendency: time expressions often come before place expressions.

So:

• heute = time
• im Kurs = place/situation

That makes heute im Kurs sound very natural.

German word order inside the middle of a clause can vary, but time before place is a very useful pattern to remember.

Yes. In German, subordinate clauses are separated by commas.

So you need a comma:

• after Obwohl ich gestern müde war
• before damit ich heute im Kurs sicherer bin

That is standard German punctuation.

Yes. German word order is flexible, as long as the verb-position rules are respected.

For example, you could also say:

• Ich habe meine Notizen noch einmal gelesen, obwohl ich gestern müde war, damit ich heute im Kurs sicherer bin.

But the original version is very natural because it highlights the contrast first:

• Although I was tired yesterday...

Starting with obwohl puts emphasis on the fact that the action happened despite being tired.

Normally, yes. Obwohl introduces a clause with its own subject and verb.

For example:

• obwohl ich müde war
• obwohl es spät war

It is not used like a preposition. So you would not use it the same way as English sometimes compresses ideas, like despite being tired. In German, that idea is usually expressed differently, for example with:

• trotz meiner Müdigkeit
• obwohl ich müde war

In your sentence, obwohl correctly introduces a full clause.