Sanskrit compound

inherits from its parent, the Proto-Indo-European language, the capability of forming compound nouns, also widely seen in kindred languages, especially German, Greek, and English.
However, Sanskrit, especially in the later stages of the language, significantly expands on this both in terms of the number of elements making up a single compound and the volume of compound usage in the literature, a development which is unique within Indo-European to Sanskrit and closely related languages.
Further, this development in the later language is an entirely artificial, literary construct and does not reflect the spoken language.

Background

In Sanskrit, as in Proto-Indo-European, a compound is formed by taking the stem-form of the first element and combining the two elements with a single accented syllable.
In the later language, this process can be repeated recursively—in theory, ad infinitum, with the freshly made compound becoming the first element of a new one.
The process of 'resolving' the compound, i.e., expounding the meaning using the component words declined as in sentence form is termed vigraha·vākya.
Broadly, compounds can be divided into two classes: endocentric and exocentric.

Endocentric compounds

An endocentric compound, usually called determinative, is where the compound is essentially the sum of its parts, the meaning being an extension of one of the parts:

blackbird → a type of black bird
White House → the official residence of the US president
siṃha·purás → lion-city
Exocentric compounds

An exocentric compound refers to something outside the components:

redhead → someone with red hair
pickpocket → someone who picks someone else's pockets
'bahu·vrīhi' → lit. 'much-rice', i.e., possessing much rice: an indication of wealth

Indeed, this term 'bahuvrihi' is used both in Sanskrit and standard Indo-European linguistics to denote this type of compound.
Sanskrit expands on these to provide several further distinctions as below:

Classification

In traditional Sanskrit grammar, compounds are divided into the following main classes:

Tatpuruṣa
* Tatpuruṣa proper
* Karmadhāraya
** Dvigu
* Nañ-tatpuruṣa
* Prādi and gati
* Upapada
Bahuvrīhi
* Dvigu
Dvandva
Avyayībhāva

The first two of these, tatpuruṣa and bahuvrīhi, are Indo-European inheritances, the latter two are Indic innovations. Alongside the term bahuvrīhi, tatpuruṣa has also been adopted in mainstream Indo-European linguistics as the technical term denoting this type of compounding.
The following sections give an outline of the main types of compounds with examples. The examples demonstrate the composition of the compound's elements, and the meanings in English generally correspond to them, in most cases being a similar compound as well. Where this is not the case or the meaning is not clear, a further resolution is provided.

''Tatpuruṣa'' (determinative)

A tatpuruṣa is an endocentric compound composed of two elements, wherein the first one, named the attributive, determines the second one.
Based on the grammatical nature of the attributive member, six varieties of tatpuruṣa compounds are identified as seen in the classification above. A further distinction is also made based on whether the attributive is in the nominative or an oblique case.

''Tatpuruṣa proper''

The first member here is an attributive in an oblique relationship with the second, and are therefore termed dependent determinatives.

Word	Meaning, resolution	Relationship
jaya·prepsu	victory-seeking	Accusative
deva·dattá-	god-given: given by the gods	Instrumental
viṣṇu·bali	Viṣṇu-offering: offering to Viṣṇu	Dative
svarga·patitá-	heaven-fallen: fallen from heaven	Ablative
vyāghra·buddhi	tiger-thought: the thought of it being a tiger	Genitive
yajur·veda-	sacrifice-knowledge: the knowledge of sacrifice	Genitive
gṛha·jata-	house-born: born in the house	Locative

''Karmadhāraya-tatpuruṣa'' (descriptive)

In a karmadhāraya-tatpuruṣa compound, the first element qualifies the second one adjectively when the latter is a noun. When the second member is an adjective, the qualification is adverbial. Other parts of speech besides adjectives and adverbs may be used to obtain the adjective or adverbial qualification.

Word	Meaning, resolution
nīlôtpala	blue lotus
sarva·guṇa	all good quality
priya·sakha	dear friend
maha·rṣí	great-sage
rajata·pātrá	silver cup

''Dvigu-tatpuruṣa'' (numerative)

In essence dvigu can refer to several compound types where the first element is a numeral. Dvigu-tatpuruṣa compounds are a special subcategory of karmadhārayas.

Word	Meaning, resolution
dvi·rājá-	two kings
tri·bhuvana-	three-world: the universe
tri·yugá-	three ages
tri·divá	the triple heaven
daśâṅgulá-	ten fingers' breadth
ṣaḍ·ahá-	six day's time
sahasrâhṇyá-	thousand days' journey

dvigu compounds of bahuvrīhi type are noted below.

''Nañ-tatpuruṣa'' (negative)

In a nañ-tatpuruṣa compound, the first element is a privative, a negator: a-, an- or na-, just like the English un-, Latin-derived in-, non- or Greek-derived a-, an- .

Word	Meaning, resolution
á·brāhmaṇa	non-Brahmin
án·aśva	non-horse: not a horse
á·pati	non-master: not a master
á·vidyā	non-knowledge: ignorance
á·kumāra	unyoung: old
á·śraddhā	unbelief, non-creed

''Upapada-tatpuruṣa''

These are composed of a second member that occurs only in a compound and cannot stand on its own. These are either roots or verbal derivatives from them.

Word	Meaning, resolution
sa·yúj	joining together
su·kṛ́t	well-doing, a good deed
kumbha·kāra-	pot-maker
sva·rā́j	self-ruling: sovereign
manu·já	Manu-born, born of Manu, man
svayam·bhū́	self-existent
eka·já	only-born
jala·dá	water-giving: a cloud
sarva·jñá	all-knowing: an omniscient person

''Aluk-tatpuruṣa''

In an aluk-tatpuruṣa compound, in contrast to the standard pattern of being in stem form, the first element takes a case form as if in a sentence:

First Element → Word	Meaning, resolution	Case
ojas → ojasā·kṛtá-	done with might	Instrumental
ātman → ātmane·pada-	'word for self': the reflexive voice	Dative
dyaus → divas·pati	'lord of the sky': a name of Indra	Genitive
yudh → yudhi·ṣṭhira-	'firm in battle': a name	Locative

''Dvandva'' (co-ordinative)

These consist of two or more noun stems connected with "and". There are mainly three kinds of dvandva pair constructions in Sanskrit:

''Itaretara-dvandva''

The result of itaretara-dvandva is an enumerative word, the meaning of which refers to all its constituent members. The resultant compound word is in the dual or plural number and takes the gender of the final member in the compound construction. Examples:

Word	Meaning, resolution
mitrā́·váruṇau	Mitra and Varuṇa
dyāvā·pṛthivī	heaven and earth
vrīhi·yavaú	rice and barley
candrādityau	moon and sun
devāsurā́s	the gods and the demons
hasty·aśvās	elephants and horses
roga·śoka·parītāpa·bandhana·vyasanāni	disease, pain, grief, bondage and adversity

''Samāhāra-dvandva''

Words may be organised in a compound to form a metonym, and sometimes the words may comprise all the constituent parts of the whole. The resultant bears a collective sense and is always singular and neutral.

Word	Literal ⇒ Meaning
pāṇi·pādam	'hands and feet' ⇒ limbs, appendages
āhāra·nidrā·bhayam	'food, sleep and fear' ⇒ vicissitudes, features of life

''Ekaśeṣa-dvandva''

Some Sanskrit grammarians identify a third kind of dvandva which they call ekaśeṣa-dvandva, where only one stem remains in what is viewed as the compound of multiple words.

Compound	Resolution	Meaning
pitarau	mātā + pitā	'mother and father' ⇒ parents
mṛgāḥ	mṛgaḥ + mṛgā	'does and bucks' ⇒ deer
putrāḥ	putrāḥ + duhitaraḥ	'sons and daughters' ⇒ children