[#DuolingoForumGems originally posted on 2021-01-16 on the Duolingo Hungarian for English speakers forum by peter.kristof.hu ] 

Lenni vagy nem lenni

The verb van has many meanings and is used in several ways. Its infinitive form is lenni. It roughly corresponds to the verbs "to be" and "to have". As an intransitive verb, it cannot have an object. To understand the use of van, we need to know the types of predicates in the Hungarian sentences.

• Simple predicate. It usually consists of one verb (but it can be more complex).
  For example:
  A vonat gyorsan halad. -- The train is moving fast.

• Complex predicate (nominal - verb). It consists of a nominal (noun, adjective, numeral, pronoun) and the conjugated lenni. It is the case when the verb van/vannak is used as an auxiliary verb, i.e. a linking verb or copula. Van/vannak is to be omitted in some cases. In these cases, it is sometimes called a nominal predicate because there is no verb.
  An example of the complex predicate:
  Te (egy) tanuló vagy. -- You are a student. You will see that the English and Hungarian approaches are slightly different.

Next, let's look at the common meanings of lenni. (Predicates are marked in bold.)

1. Describing the existence of a thing
We express the existence of a thing, so we don't describe an attribute, we don't specify. In this use, it is a main verb, forming a simple predicate.

The word nincs/nincsenek is used to negate an existence in the present tense. In the past tense it is nem volt/nem voltak, in the future tens nem lesz/nem lesznek.

1.a These sentences make a general statement.

Van igazság (a földön). -- There is truth (in the world).

That is

Topic	Comment
	Van igazság (a földön).

Or according to subject-predicate analysis:

Predicate	Subject
Van	igazság	(a földön).

Van Isten -- God exists.
Van leves (ebédre). -- There is soup (for lunch).
Vannak még hibák. -- There are still mistakes.
Nincs kardfogú tigris. -- There is no saber toothed tiger.

1.b The following sentences are very similar to the previous ones. They are natural and environmental states and structures expressing the situation.

(Egész nap) szép idő van. -- It is nice weather (all day).

Topic	Comment
	(Egész nap) szép idő van.

Béke van (a földön). -- There is peace (in the world).
Meleg van (a szobában). -- It is warm (in the room).
Reggel van. -- It is morning.
Gondok vannak. -- There are problems.
Gondolkodom, tehát vagyok. -- I think, therefore I am.

Notice that we expose the verb van/vannak in the third person unlike the later particular cases.

Some of the sentences above begin with a verb. These and other forms of sentences are so-called thetic sentences in which it is peculiar that there is no topic. (The topic is the theme of a discourse that we have to introduce it in the previous.) The predicate van/vannak does not require any other complement than the subject.

For comparison, here are similar sentences using another verb than "van":
Jön a vonat. -- The train is coming.
(Meg)jött a vonat. -- The train has came.

2. Describing quality or identification
"Lenni" is the verbal part of a complex predicate here. In this case, in the indicative mode, present tense, third-person van/vannak to be omitted. In the following sentence "Ø" indicates the abandoned verb.

• Noun + "lenni"
  Ő tanuló Ø . -- He is a student.

(Én) tanuló vagyok.	(Mi) tanulók vagyunk.
(Te) tanuló vagy.	(Ti) tanulók vagytok.
Ő tanuló Ø.	Ők tanulók Ø.

The personal pronoun can also be omitted in a third person if the context exposes the meaning.

A sas (egy) madár Ø. -- The eagle is a bird.
Kati Ø a barátnőm -- Kati is my girlfriend.

• Adjective + "lenni"
  A felhőkarcolók magasak Ø. -- The skyscrapers are high.
  Egész nap szép Ø az idő. -- The weather is nice all day.

Put the sentence in other tenses for testing.
Past tense:
Egész nap szép volt az idő. -- The weather was nice all day.
Future tense:
Egész nap szép lesz az idő. -- The weather will be nice all day.

• Numeral + "lenni"
  Kétszer kettő négy Ø. -- Twice two is four.
  Én vagyok az első. -- I am the first.

• Pronoun + "lenni"
  Ez a könyv az enyém Ø. -- This book is mine.
  Mi van veled? -- What about you?

3. Adverb + "lenni" It is most often an adverb of place.
A húsa sütőben van. -- The meat is in the oven.
István itthon van. -- István is at home.
Ez a játék fából van. -- This toy is made of wood.
Úgy van. -- That's right.
Az üzlet nyitva van. -- The store is open.

In some cases, van/vannak may be omitted, but not necessarily:
Itt (van) a könyved. -- Here is your book.
A kulcs a lábtörlő alatt (van). -- The key is under the doormat.
Kinn (van) a bárány, benn (van) a farkas. -- The lamb is out there, the wolf inside.
Jobbra (van) a kocsma -- To the right is the pub.

4. Possession Van plays a related role between the possessive and the possessed object as a main verb. It expresses both existence and possession at the same time. Here, van is a main verb forming a simple predicate. The possessed think is the subject of the sentence, and the possessor is a dative complement of the verb. In the singular of the possessed word the verb form is van, and in the plural, vannak in all person. (The suffix of the possessed word indicates the person and number, but it is a separate topi

Van (nekem) egy lányom. -- I have a daughter.
A lónak négy lába van. -- The horse has four legs.
(Neki) van pénze. -- She has money.
The conjugation of this:

(nekem) van pénzem	(nekünk) van pénzünk
(neked) van pénzed	(nektek) van pénzetek
(neki) van pénze	(nekik) van pénzük

5. Other uses

Van hol aludni. -- There is a place to sleep.
Nálad van a kulcs? -- Do you have the key?
etc.
(The Thesaurus of the Hungarian language describes dozens more meanings.)

Sources:
http://gepeskonyv.btk.elte.hu/adatok/Magyar/31Lakatos/Digi_TK_v2/Mondattan/all_minta.htm
http://mnytud.arts.unideb.hu/ot/5/ot5_10kadare.pdf
http://acta.bibl.u-szeged.hu/54312/1/mai_magyar_nyelv_006_053-062.pdf

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P.S.
A small dictionary for those who may want to read grammatical texts in Hungarian (grammatical terms)

alany - subject
állítmány - predicate
tárgy - direct object/object
részeshatározó - indirect object
bővítmény -- complement
vonzat -- argument
névszó - nominal
tárgyas ige - transitive verb
tárgyatlan ige - intransitive verb
igeragozás - conjugation
névszóragozás - inflection