Learn Hardcore Esperanto: Mi havas tri librojn.

Mi havas tri librojn. = I have three books.
(no article needed; they’re just some three books)
Mi havas la tri librojn. = I have the three books.
(the speaker and listener know which specific three)

If you wanted to say some books without a number, you could say:

Mi havas kelkajn librojn. = I have some books.
but with an exact number (tri) you just say tri librojn with no article.

Could I change the word order, like Tri librojn mi havas or Mi tri librojn havas?

Yes, Esperanto word order is relatively flexible because the -n shows what is the direct object.

All of these are grammatically possible:

Mi havas tri librojn. (most neutral, standard S–V–O order)
Tri librojn mi havas. (emphasis on three books; like “It’s three books that I have.”)
Mi tri librojn havas. (also possible, slightly marked or emphatic)
Tri librojn havas mi. (quite marked/poetic)

For everyday speech and writing, Mi havas tri librojn is by far the most natural choice.

How is havas formed, and does it change with I/you/he like English have/has?

The verb havas comes from the root hav- plus the present-tense ending -as.

havi = to have (infinitive)
havas = have/has (present)
havis = had (past)
havos = will have (future)
havus = would have (conditional)
havu = have! (command/wish form)

Esperanto verbs do not change by person or number.
So you say:

Mi havas = I have
Vi havas = you have
Li/ŝi/ĝi havas = he/she/it has
Ni havas = we have
Ili havas = they have

Same havas for everyone.

Does Mi havas tri librojn mean I own them, or just that I physically have them right now?

Havi mainly expresses possession in a broad sense: that the books belong to you or are in your possession.

Depending on context, it can mean:

Legal ownership
Long-term possession (e.g., books you keep at home)
Short-term possession (e.g., books you’ve borrowed)

If you specifically mean you are holding them in your hands at the moment, Esperanto often uses teni:

Mi tenas tri librojn. = I am holding three books.

But in many contexts, Mi havas tri librojn could also be understood as “I have three books on me / with me” if the situation makes that clear.

Why is Mi capitalized? Is the pronoun mi always written with a capital letter like English I?

No. In Esperanto, mi is normally not capitalized. It’s only capitalized here because it is the first word of the sentence.

Mi havas tri librojn.
Hieraŭ mi vidis lin. = Yesterday I saw him.

Unlike English I, Esperanto mi is lowercase in the middle of a sentence:

Hieraŭ mi legis tri librojn. = Yesterday I read three books.

Can I drop Mi and just say Havas tri librojn, like Spanish Tengo tres libros?

In standard Esperanto, you normally keep the subject pronoun.
So Havas tri librojn by itself sounds like a fragment or a headline, not a normal sentence.

Typical full sentence:

Mi havas tri librojn.

You might see subject pronouns omitted:

In titles, notes, or telegraphic style (e.g., on labels or lists)
In some poetry or very informal shorthand

But for ordinary speech or writing, you should say Mi havas tri librojn.

How do you pronounce librojn, especially the ojn part?

librojn is pronounced roughly like “LEE-broyn”:

li = like lee
bro = like bro in brother (but a trilled or tapped r)
jn = the j is like English y, and ojn together sounds like oyn in boyn (not a real word, but that sound)

Details:

j = like y in yes
o = a pure o sound, like in Italian or Spanish (not like English “oh” diphthong)
n = normal n
Stress is on the next-to-last syllable, so LÍ-brojn.

So: MI HÁ-vas TRÍ LÍ-broyn.

If I add an adjective, does it also get -j and -n, like the noun?

Yes. In Esperanto, adjectives agree with the nouns they describe in number and case.

So:

libro = book
bela libro = a beautiful book

Plural:

belaj libroj = beautiful books

Accusative plural (as in your sentence):

Mi havas tri belajn librojn.
- bel-a-j-n (root + adjective + plural + accusative)
- libr-o-j-n

Both the adjective belajn and the noun librojn show -j (plural) and -n (accusative).

Do numbers like tri ever change form for plural or case, like trij or trin?

Normally, no. The basic cardinal numbers (unu, du, tri, kvar, …) are invariable in standard usage:

tri libroj (subject)
tri librojn (object)
kun tri libroj (with three books)

The noun carries the plural -j and accusative -n, not the numeral:

Mi havas la tri librojn. = I have the three books.

So you do not say trij libroj or trin librojn in normal Esperanto. The endings go on the last word of the noun phrase (here, the noun and any adjectives), not on the number itself.

Why is there no word like some in Mi havas tri librojn if the books aren’t specific?

Once you give an exact number (tri), Esperanto doesn’t need an extra word like some. The number already tells you how many.

Mi havas tri librojn. = I have three books.
(they are just some three books; not specific ones)
Mi havas iom da libroj. = I have some books (an unspecified amount).
Mi havas kelkajn librojn. = I have several/some books.

If the books are specific, you show that with la or a demonstrative like tiuj:

Mi havas la tri librojn. = I have the three (known) books.
Mi havas tiujn tri librojn. = I have those three books.