Voy a seguir estudiando español hasta el final del semestre.

Voy a + infinitive is a very common way to talk about the future in Spanish, especially in everyday speech.

So:

• Voy a seguir estudiando español = I’m going to keep studying Spanish
• Seguiré estudiando español = I will keep studying Spanish

Both are correct. In many contexts, the difference is small. Voy a seguir often sounds a bit more immediate, personal, or planned, while seguiré can sound a little more formal or neutral.

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

• Voy already means I go / I am going
• So yo is not necessary

You could say Yo voy a seguir estudiando español..., but that would usually add emphasis, contrast, or clarity.

For example:

• Yo voy a seguir estudiando español, pero mi amigo no.
  = I’m going to keep studying Spanish, but my friend isn’t.

Seguir + gerund means to keep doing something or to continue doing something.

So:

• seguir estudiando = to keep studying / to continue studying

This structure is very common in Spanish:

• Sigo trabajando = I keep working
• Vamos a seguir hablando = We’re going to keep talking

In your sentence, voy a seguir estudiando means I’m going to continue studying.

Because after seguir, Spanish normally uses the gerund to express continuing an action already in progress.

• seguir estudiando = to continue studying
• not normally seguir estudiar

So the pattern is:

• seguir + gerund

Examples:

• Sigue lloviendo = It keeps raining
• Seguimos esperando = We keep waiting

The form estudiando is the gerund of estudiar.

Estudiando is the gerund of estudiar.

In English, the gerund/participle often looks like the -ing form, and this is often a helpful comparison:

• estudiar = to study
• estudiando = studying

In Spanish, the gerund is often used after verbs like:

• estar → estoy estudiando = I am studying
• seguir → sigo estudiando = I keep studying

In Spanish, names of languages are normally written with a lowercase letter.

So:

• español
• inglés
• francés

This is different from English, where you write Spanish, English, French with capitals.

The only time it would be capitalized is if it comes at the beginning of a sentence.

After verbs like hablar, estudiar, aprender, and enseñar, Spanish often uses language names without an article.

So:

• Estudio español = I study Spanish
• Habla inglés = He/She speaks English

This is the normal pattern here.

You can use the article in other contexts, for example when talking about the language in a more general or specific way:

• El español es una lengua muy extendida.
  = Spanish is a very widespread language.

But in your sentence, estudiando español is exactly what you would expect.

Literally, it breaks down like this:

• hasta = until / up to
• el final = the end
• del semestre = of the semester

So the whole phrase means:

• until the end of the semester

It gives the time limit for how long the action will continue.

Because de + el contracts to del in Spanish.

So:

• de + el = del

Examples:

• el final del semestre = the end of the semester
• la puerta del coche = the door of the car

This contraction is normally required.

A similar contraction also happens with a + el = al:

• Voy al centro = I’m going to the center

Yes, but hasta el final del semestre sounds fuller and very natural.

• hasta el final del semestre = very clear, standard, and natural
• hasta fin de semestre = also possible, but a bit more compressed and less neutral in some contexts

For a learner, hasta el final del semestre is an excellent choice.

Yes, semestre is completely correct and understood in Spain.

That said, depending on the school or university system, you may also hear other academic terms such as:

• trimestre = trimester / term
• cuatrimestre = four-month term
• curso = school year / academic year

But if you specifically mean semester, then semestre is the right word.

Yes. That is also correct and natural.

Compare:

• Voy a seguir estudiando español...
• Seguiré estudiando español...

Both mean basically the same thing here. The first is often more common in everyday speech, while the second uses the simple future tense.

A learner should understand both.

Very often, yes, but it can also mean up to depending on context.

Examples:

• Hasta mañana = Until tomorrow / See you tomorrow
• Trabajo hasta las seis = I work until six
• Caminamos hasta la estación = We walked up to the station

In your sentence, hasta clearly means until because it refers to time:

• hasta el final del semestre = until the end of the semester