Antes de escrever a introdução, eu gosto de fazer um pequeno resumo do tema.

Because antes de is the normal structure in Portuguese for before when it is followed by a verb.

• antes de + infinitive = before doing something
• antes de escrever = before writing

So the de is required here.

Examples:

• Antes de sair, feche a porta. = Before leaving, close the door.
• Antes de dormir, eu leio. = Before sleeping, I read.

After the preposition de, Portuguese normally uses the infinitive form of the verb.

So:

• antes de escrever = before writing

Not:

• antes de escrevo
• antes de escreve

This is very similar to English structures like before writing rather than before I write, although Portuguese can also express before I write in other ways depending on the sentence.

Introdução is a feminine noun, so its singular definite article is a.

• a introdução = the introduction

Portuguese uses definite articles more often than English does. In this sentence, a introdução sounds natural because it refers to a specific introduction: the introduction of the text, paper, or work being discussed.

Also:

• introdução is feminine
• so: a introdução
• not o introdução

No, eu is optional here.

Portuguese often leaves out subject pronouns because the verb form already shows who the subject is.

So both are natural:

• Antes de escrever a introdução, eu gosto de fazer um pequeno resumo do tema.
• Antes de escrever a introdução, gosto de fazer um pequeno resumo do tema.

Including eu can add:

• emphasis
• clarity
• contrast

For example, if you want to stress I in contrast with someone else, keeping eu makes sense.

Because the verb is gostar de, not just gostar.

So Portuguese says:

• gostar de algo = to like something
• gostar de fazer algo = to like doing something

Examples:

• Gosto de café. = I like coffee.
• Gosto de estudar. = I like studying.

So in your sentence:

• eu gosto de fazer = I like to do / I like doing

The de is part of the verb pattern and must stay there.

Literally, it means I like to do. But in context, it often suggests a personal habit or preferred way of doing things.

So here, it can imply:

• I like to make a short summary before writing the introduction
• and also naturally suggest this is something I tend to do

It does not necessarily mean strong emotional enjoyment. Sometimes gosto de simply expresses preference or usual practice.

Both are possible in Portuguese, but they can sound slightly different.

um pequeno resumo is the most natural choice here and usually means:

• a brief summary
• a short little summary

When pequeno comes before the noun, it often has a more subjective or descriptive feel.

um resumo pequeno is grammatically possible, but it sounds more literal, as if you are emphasizing the size/length of the summary in a more objective way.

In this sentence, um pequeno resumo is the idiomatic choice.

Do is a contraction of:

• de + o = do

So:

• do tema = of the topic / about the topic

Portuguese very commonly contracts de with definite articles:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das

So:

• resumo do tema = summary of the topic
• not normally resumo de o tema

Here, tema is better understood as:

• topic
• subject
• sometimes theme

In an academic or writing context, tema often means the subject being discussed in the text.

So resumo do tema means something like:

• a brief summary of the topic
• a short summary of the subject matter

Although theme is a possible translation, in many everyday learning contexts topic or subject sounds more natural in English.

The part Antes de escrever a introdução is an introductory phrase. In Portuguese, it is very common to separate that kind of opening phrase from the main clause with a comma.

So the sentence is divided like this:

• Antes de escrever a introdução, = introductory time phrase
• eu gosto de fazer um pequeno resumo do tema. = main statement

The comma helps readability and is the standard written form here.

Yes, but some versions sound more natural than others.

The original order is very natural:

• Antes de escrever a introdução, eu gosto de fazer um pequeno resumo do tema.

You could also say:

• Eu gosto de fazer um pequeno resumo do tema antes de escrever a introdução.

This keeps the same basic meaning. The difference is mainly one of emphasis:

• starting with Antes de escrever a introdução emphasizes the time/order first
• starting with Eu gosto de fazer... emphasizes the speaker’s preference or habit first

Both are correct and natural.