Soy tan despistado que ayer fui a la biblioteca sin el cuaderno.

Because ser is used for a more general, characteristic quality, while estar is used for a temporary state.

• Soy despistado = I’m absent-minded / forgetful as a trait.
• Estoy despistado = I’m confused / out of it right now, in this moment.

So Soy tan despistado que... means something like I’m so absent-minded that..., describing the speaker’s usual nature, not just a temporary feeling.

Tan ... que means so ... that.

It is a very common pattern in Spanish:

• tan
  • adjective/adverb + que
• so
  • adjective/adverb + that

In this sentence:

• tan despistado = so absent-minded
• que ayer fui a la biblioteca sin el cuaderno = that yesterday I went to the library without the notebook

More examples:

• Es tan alto que no cabe por la puerta. = He’s so tall that he can’t fit through the door.
• Habla tan rápido que no entiendo nada. = She speaks so fast that I don’t understand anything.

Despistado is a very common Spanish word meaning things like:

• absent-minded
• forgetful
• scatterbrained
• sometimes clueless or distracted, depending on context

In this sentence, it clearly means forgetful / absent-minded.

It is often used in everyday speech and is usually fairly mild, not especially harsh. Calling yourself despistado sounds natural and conversational.

Because the adjective has to agree with the speaker’s gender.

• A male speaker would say Soy tan despistado...
• A female speaker would say Soy tan despistada...

If the subject were plural:

• Somos tan despistados... = We’re so absent-minded... (mixed group or masculine)
• Somos tan despistadas... = We’re so absent-minded... (all female)

Fui is the preterite of ir, and here it is used because the speaker is referring to a completed action at a specific time:

• ayer = yesterday
• fui = I went

So the sentence presents one finished event: yesterday, the speaker went to the library without the notebook.

If you used iba, it would sound more like background information, habit, or an action in progress in the past:

• Ayer iba a la biblioteca... = Yesterday I was going to the library... or I used to go... depending on context

That does not fit as well here, because the speaker is giving one concrete example of being absent-minded.

Because the sentence combines:

1. a general truth about the speaker
2. a specific example from yesterday

So:

• Soy tan despistado... = I’m so absent-minded... → general characteristic
• ...que ayer fui... = ...that yesterday I went... → specific past event proving it

This is perfectly normal in both Spanish and English.

Because Spanish normally uses the definite article with many places:

• ir a la biblioteca = to go to the library
• ir al cine = to go to the cinema
• ir al banco = to go to the bank

Here:

• a = to
• la biblioteca = the library

So a la biblioteca is exactly what you would expect.

Also, a + la stays a la. It only contracts with el:

• a + el = al
• but a + la = a la

Spanish often uses the definite article (el / la / los / las) where English would use a possessive like my.

So sin el cuaderno can naturally mean:

• without the notebook
• or, in context, without my notebook

Since it is obvious whose notebook is meant, Spanish does not always need mi.

Compare:

• Me duele la cabeza. = My head hurts.
• He olvidado las llaves. = I’ve forgotten my keys.

You could say sin mi cuaderno, and that would also be correct. It just sounds a bit more explicit.

Yes, but it changes the feel slightly.

• sin el cuaderno suggests a specific notebook, the one the speaker was supposed to bring
• sin cuaderno is more general: without a notebook / without notebook

In this sentence, sin el cuaderno sounds more natural because it refers to the particular notebook the speaker forgot.

Because Spanish usually drops subject pronouns when the verb already makes the subject clear.

• Soy already tells you it means I am
• Fui already tells you it means I went

So yo is unnecessary unless you want emphasis or contrast.

For example:

• Yo soy tan despistado que... sounds more emphatic, like I’m so absent-minded that...
• Without yo, it is the normal neutral version.

Yes. Spanish word order is flexible.

These are all natural:

• Soy tan despistado que ayer fui a la biblioteca sin el cuaderno.
• Ayer fui a la biblioteca sin el cuaderno porque soy muy despistado.
• Soy tan despistado que fui ayer a la biblioteca sin el cuaderno.

The original version is very natural because it sets up the idea first (I’m so absent-minded) and then gives the example (yesterday I went...).

Usually no. It is generally a mild, everyday word.

If someone says:

• Soy muy despistado
• Es un poco despistado

it usually means they are forgetful, distracted, or not very attentive. It often sounds almost affectionate or self-deprecating rather than insulting.

A much stronger insult would use different words.

Yes. A few natural alternatives are:

• Soy tan despistado que ayer fui a la biblioteca y me dejé el cuaderno en casa.
  I’m so absent-minded that yesterday I went to the library and left the notebook at home.

• Soy tan despistado que ayer fui a la biblioteca sin mi cuaderno.
  More explicit with mi.

• Ayer fui a la biblioteca sin el cuaderno. Qué despistado soy.
  Yesterday I went to the library without the notebook. I’m so absent-minded.

But the original sentence is already completely natural and idiomatic.