Learn Hardcore Latin: Puer aquam frigidam bibere non vult, sed mater ei aquam calidam dat. - The boy does not want to drink cold water, but mother gives him warm water.

puer – the boy (subject, nominative singular)
aquam – water (direct object, accusative singular)
frigidam – cold (adjective modifying aquam, accusative singular feminine)
bibere – to drink (infinitive)
non – not
vult – wants (3rd person singular of velle, to want)
sed – but
mater – the mother (subject of the second clause, nominative singular)
ei – to him (indirect object, dative singular)
aquam – water again (direct object)
calidam – hot / warm (adjective modifying aquam, accusative singular feminine)
dat – gives (3rd person singular of dare, to give)

Why is it puer and not puerum?

Puer is in the nominative case because it is the subject of the verb vult (the boy wants).

puer (nominative singular) – used for the subject: the boy.
puerum (accusative singular) – would be used as a direct object (the boy as something acted on), which is not the case here.

So puer = the boy (who does something), not the boy (whom something happens to).

Why is it aquam frigidam and not aqua frigida?

Because here aquam is the direct object of bibere (to drink), so it must be in the accusative case:

aqua frigida – nominative or ablative (e.g. the water is cold / with cold water).
aquam frigidam – accusative, used when the water is what you drink, see, carry, etc.

Both the noun (aquam) and the adjective (frigidam) must match in:

case: accusative,
number: singular,
gender: feminine.

So aquam frigidam literally: cold water as the thing being drunk.

Why is bibere in the infinitive form? Why not a finite verb like bibit?

Latin normally expresses want to do something with velle + infinitive:

puer bibit aquam – the boy drinks water (simple statement).
puer aquam bibere vult – the boy wants to drink water.

Vult (he wants) needs an infinitive (bibere, to drink) as its complement.
Using vult bibit would be ungrammatical in Classical Latin; you do not put two finite verbs together like he wants drinks.

Where does non go, and could I put it somewhere else?

In this sentence it is non vult: does not want.

The most standard position is non immediately before the word it negates, very often the main verb:
- puer aquam frigidam bibere non vult – the boy does not want to drink cold water.

You can sometimes change the order a bit, but for a learner you should stick with non directly before the verb:

non puer vult... would sound like it is not the boy who wants... (focus on puer), which is a different nuance.

What does vult come from? It doesn’t look like a regular verb.

Vult is the 3rd person singular present of velle (to want), which is an irregular verb.

Key forms (present tense):

volo – I want
vis – you want
vult – he/she/it wants
volumus – we want
vultis – you (pl.) want
volunt – they want

So puer ... non vult = the boy does not want.

What is the function of sed here?

Sed is a coordinating conjunction meaning but.

It connects two clauses that contrast with each other:

Puer aquam frigidam bibere non vult – The boy does not want to drink cold water
sed mater ei aquam calidam dat – but the mother gives him hot water.

Latin often uses sed much like English uses but at the beginning of the second clause.

Why is it mater ei aquam calidam dat and not mater eum aquam calidam dat?

Because ei is in the dative case and means to him, while eum is accusative and means him (as a direct object).

Here:

aquam calidam is the direct object (what is given),
ei is the indirect object (the person who receives it).

So:

mater ei aquam calidam dat – the mother gives hot water to him.
mater eum videt – the mother sees him (here eum is the direct object).

Latin uses the dative for the indirect object without a preposition, where English uses to or for.

What exactly does ei mean, and what is its dictionary form?

Ei here means to him.

It is the dative singular of the 3rd person pronoun. The usual dictionary form is is, ea, id (he, she, it).

In the masculine singular:

is – he (nominative)
eius – of him, his (genitive)
ei – to/for him (dative)
eum – him (accusative)
eo – by/with/from him (ablative)

So ei is the correct form to use after verbs like dat (gives) when you mean to him.

Why is it calidam and not calidum or calidus?

The adjective calidus, -a, -um (hot, warm) must agree with aquam in:

gender: feminine,
number: singular,
case: accusative.

Aquam is feminine accusative singular, so:

masculine: calidus (nom. sg.), calidum (acc. sg.)
feminine: calida (nom. sg.), calidam (acc. sg.)

Therefore, aquam calidam (hot water as a direct object) is correct: both are accusative singular feminine.

Does the order aquam frigidam and aquam calidam matter? Could I say frigidam aquam?

Latin word order is relatively flexible.

Both:

aquam frigidam
frigidam aquam

are grammatically correct; the adjective still agrees with the noun in case, number, and gender.

Very roughly:

aquam frigidam is more neutral and common,
frigidam aquam can give a bit more emphasis to frigidam (cold water, as opposed to some other kind).

For learners, putting the adjective after the noun (aquam frigidam) is a good default.

Why is there no word for “to” before ei in Latin?

Latin usually does not use a preposition like to before an indirect object.
Instead, it uses the dative case:

mater ei aquam dat – literally: the mother to-him water gives.
English needs to: the mother gives water to him.

So the ending (or form) of ei itself shows the “to” meaning; no extra preposition is needed.

Are vult and dat in the same tense?

Yes. Both are 3rd person singular, present tense, active voice:

vult – he/she/it wants
dat – he/she/it gives

So the whole sentence is describing actions in the present time:

The boy does not want to drink cold water, but the mother gives him hot water.

Could I change the word order to puer aquam frigidam non vult bibere? Is that still correct?

Yes, puer aquam frigidam non vult bibere is still grammatically correct.

Latin allows:

puer aquam frigidam bibere non vult
puer aquam frigidam non vult bibere

Both can mean the boy does not want to drink cold water.
The most standard and clearest for learners is non right before vult, as in the original sentence.