Después del examen, quiero volver a estar tranquilo.

Because de + el contracts to del in Spanish.

• después de = after
• el examen = the exam
• So: después del examen = after the exam

This contraction is required with de + el.
Compare:

• después del partido = after the match
• la casa del profesor = the teacher’s house

A similar contraction happens with a + el = al.

Después de means after when it is followed by a noun.

In this sentence, it is followed by el examen, so:

• después del examen = after the exam

Useful comparison:

• después de + noun
  
  • después del trabajo = after work
• después de que + clause
  
  • después de que termine el examen = after the exam finishes / after the exam is over

So here, después del examen is the simpler noun-based structure.

Spanish often leaves out subject pronouns because the verb ending already shows who the subject is.

• quiero = I want
• The -o ending tells you it is yo

So:

• (Yo) quiero volver a estar tranquilo

Both are correct, but yo is usually omitted unless you want emphasis, contrast, or clarity.

For example:

• Yo quiero volver a estar tranquilo, pero ella no.
  = I want to feel calm again, but she doesn’t.

Volver a + infinitive means to do something again.

So:

• volver a estar = to be again
• quiero volver a estar tranquilo = I want to be/feel calm again

This is a very common structure:

• volver a intentar = to try again
• volver a leer = to read again
• volver a empezar = to start again

In this sentence, it suggests the speaker was calm before, then stopped being calm, and now wants that state back.

Because estar is used for a temporary state or condition, while ser is used more for essential characteristics.

Here, the idea is to feel calm or to be calm for the moment, especially after the stress of an exam. That is why estar is the natural choice.

• estar tranquilo = to be calm / to feel calm
• ser tranquilo = to be a calm person by nature

Compare:

• Después del examen, quiero estar tranquilo.
  = After the exam, I want to feel calm.
• Soy una persona tranquila.
  = I’m a calm person.

Tranquilo agrees with the person it describes.

If the speaker is male, you use:

• tranquilo

If the speaker is female, you use:

• tranquila

So:

• Después del examen, quiero volver a estar tranquilo.
  = said by a man
• Después del examen, quiero volver a estar tranquila.
  = said by a woman

If you are talking about more than one person, the adjective changes too:

• tranquilos
• tranquilas

It can mean both, depending on context.

In English, we often say:

• to be calm
• to feel calm

Spanish uses estar tranquilo for this kind of temporary emotional state, so both translations can work.

In this sentence, feel calm again may sound especially natural because it refers to the speaker’s emotional state after the exam.

Grammatically, volver a estar tranquilo is much more natural here.

That is because volver a + infinitive is the normal pattern for doing something again.
Regresar usually means to return in a physical or figurative sense, but it is not the usual choice for again before another verb.

So:

• quiero volver a estar tranquilo = natural
• quiero regresar a estar tranquilo = understandable, but less idiomatic here

If you want to say return to a calm state, you could also say:

• quiero recuperar la tranquilidad
• quiero volver a sentirme tranquilo

The comma separates the introductory time phrase from the main clause:

• Después del examen, = introductory phrase
• quiero volver a estar tranquilo. = main statement

In Spanish, this comma is common and helps readability. In short sentences, some writers might omit it, but using it here is perfectly good style.

Yes. In normal use, it can cover both ideas.

It can refer to:

• the time following the exam
• the moment when the exam has finished

So in context, it often means something like:

• After the exam
• Once the exam is over

Spanish does not need to spell out that distinction unless the speaker wants to be more precise.

Yes. That is also correct.

• volver a estar tranquilo
• estar tranquilo otra vez

Both can mean to be calm again.

A small nuance:

• volver a + infinitive is a very standard way to express again
• otra vez can sound a bit more direct or emphatic in some contexts

So both are natural:

• Quiero volver a estar tranquilo.
• Quiero estar tranquilo otra vez.

Very often, yes. Examen is the standard word for exam/test in many contexts.

In Spain, people also very commonly use examen in school and university contexts:

• Tengo un examen mañana. = I have an exam tomorrow.

Depending on context, you might also hear:

• prueba = test
• control = quiz/test in some school contexts

But in your sentence, examen is completely natural.

The sentence breaks down like this:

• Después del examen = after the exam
• quiero = I want
• volver a estar = to be again
• tranquilo = calm

So the structure is:

time expression + main verb + verbal expression + adjective

More literally:

After the exam, I want to be calm again.

Or more naturally:

After the exam, I want to feel calm again.