Adverbs in Irish are unchangeable (no declension or conjugation).
Those adverbs derived from adjectives cam however be incremented (the form is the same as the adjective)

word order

The adverb comes mostly:

• before simple personal- or prepositional pronouns as the object
  e.g.: Bhí mo mhac inné agam = My son was yesterday by me.
• after emphatic pronouns ( -sa, féin, seo)
  e.g. Bhí mo mhac agamsa inné = My son was by me yesterday.
• it can, like every other part of speech, move to the beginning  (as a copular construction), the rest as a dir. relative clause
  (Is) inné a bhí mo mhac agamsa. = Yesterday, my son was by me.
  Inné (is ea) a bhí mo mhac agamsa. = Yesterday, my son was by me.

locational and directional adverbs (dobhriathra treo agus suímh)

Notice the common quartering, depending on a state of being (adverbs begin often with th-), a movement towards the speaker (s-) or a movement away from the speaker (an-) is occurring.
By expressing a relative location to anothern thing/person, adverbs can also begin with las-/lais- (laistigh, lastoir, etc). The point of reference is then inserted with de (lastuas den staighre = above the stairs, lastuaidh den tir = north of the country)
Instead, the forms with las- are also common as forms with the noun taobh: taobh thiar de = west of, taobh istigh de = within.
The difference between an- and s- is about the same as the German her- and hin-, but in other composition (anuas = down from above, síos = down below)

A following noun may be included (e.g. anuas an staighre = downstairs).
In this case, the adverbs are used as prepositions.
Additionally, one can use these adverbs as adjectives (an teach thuaidh = the northern house, an Pol Thuaidh = the North Pole).

A possibility of substantiation is prefixing an taobh: e.g. an taobh istigh = the inside, an taobh thuas = the upper, an taobh theas = the southern part

The compass (an compás)

The terms for West and East are much more often used in Irish than in English or German.
One doesn't just go "down" a street, no - one says the actual direction:
Tá mé ag dul siar an bóthar = I'm going down the road (to the West)
North and South in such sentences is often replaced by "up" (South) and "down" (North).
Tá mé ag dul síos an bóthar = I'm going down the road(to the North)

In Connacht (Cois Fhairrge) ó dheas and ó thuaidh apply independent of the direction(= from/to/in the South / North).
aduaidh and aneas are used in compound directions, independent of the direction:
e.g.: siar aduaidh = to the Northwese, thoir aneas = in the Southeast
Wind directions are generally termed as aneas, aduaidh : an gaoth aduaidh = northerly wind

Directions like "south-southwest" are formed similarly to those above, but as "southwest-south": theas thiar theas = in the south-southwest, aneas aniar aneas = from the south-southwest.

The noun forms of the directions differ greatly:
tuaisceart = North, deisceart = South,
oirthear = East, iarthar = West
oirdheisceart = Southeast, iardheisceart = Southwest
oirthuaisceart = Northeast, iarthuaisceart = Northwest

up and down

up (thuas) is often said in place of in the South and down (thíos) in place of in the North.

Aside from noun phrases like an taobh thuas = the upside there are a few others: an t-íochtar = the lower, an t-Uachtar = the upper.

front and back

"back" and "in the West" are the same (thiar)
(In Ireland one has so to say the West always at your back, so one is always looking east, "ex oriente lux"). Following this logic, "East"(thoir) = "front". Which is correct, but is hardly used this way.
Instead, one uses mostly ar aghaidh, ar tosach and other expressions.

left and right

If one follows the aforementioned behind me is the West and in front of me the East, then right of me is South:

and it is so!:  rechts = deas (comp. ó dheas = in the South).
Links = clé doesn't quite fit in this picture, but (links = tuathal is at least in the dictionary, comp. ó thuaidh = in the North)

Deas and clé are adjectives, adverbially only as ar taobh deas/clé, ar taobh na láimhe deise/clé or ar dheis/clé (deis and clé as nouns in the sense of right/left hand, instead of ar, also other prepositions are used to indicate direction)
Clé kann auch einfach so adverbial verwendet werden.

Note the threefold meaning of deas (right, southern, nice)

here and there

in and out

temporal adverbs (dobhriathra ama)

anois now	ansin then
inniu today	anocht tonight
inné yesterday	aréir last evening
arú inné day before yesterday	arú aréir the evening before last
amáireach tomorrow	anuraidh last year
arú amáireach day after tomorrow	arú anuraidh year before last

adverbs out of adjectives (dobhriathra aidiachtacha)

forming with the adverbial particle go:

go is omitted mostly:

• if there is an additional adverb, e.g.:
  D'oibrgh sé reasúnta dona = He worked pretty poorly. (comp.: D'oibrigh sé go sciobtha = He worked poorly.)
  Deirim sin minic go leor = I say it often enough (comp.: Deirim sin go minic = I say it often)
• if the adverb modifies an adjective, e.g.:
  go measartha = especially
  an teach measartha mór = the especially large house
• in copular clauses, e.g.:
  Ní dona a d'oibrgh sé = He didn't work poorly
• In the comparative (instead níos), e.g.:
  D'oibrigh sé níos measa = He worked poorer
• before the prefix ró- e.g.:
  D'oibrigh sé ródhona = He worked too poorly

The adverbial particle go is identical to the preposition go.
If it is identical to go = to/until or with the today seldomly used go = with, there are conflicting sources; more likely is go = to/until, because no eclipsis follows. Also go mór = lit. approx.: "up to [a] large [degree]"

adverbial pronouns (forainmneacha dobhriathartha)

Adverbial pronouns are formed with the help of prepositions. In German e.g. darin, darauf, hierin, deswegen, etc.

with conjugable prepositions

Many prepositions are conjugated and form prepositional pronouns. The 3rd person singular masc. of these are used as adverbs.
(exception is idir = between. There one uses the 3rd person plural.)
e.g.: aige = with it(lit.: "by-him"), air = on it(lit.: "on-him"), ann = therein (lit.: "in-him"), eatarthu = between (lit.: "between-them")

Often a demonstrativ pronoun follows, especially if a stronger meaning is desired:
sin (= that, equiv. to the dt. prefix da-/dar-): air sin = on that, dó sin = to that, de sin = of that, ann sin = in that
seo (= this, equiv. to the dt. prefix hier-): air seo = on this, dó seo = to this, de seo = of this, ann seo = in this
siúd (= that there, equiv. to the dt. prefix there(dar)-): air siúd = on that there, dó siúd = thereto, de siúd = from there, ann siúd = in there

preposition	adverb	Deutsch		preposition	adverb	Deutsch
ag	aige (sin)	at (that)		i	ann (sin)	in (that)
ar	air (sin)	upon (that)		idir	eatarthu (sin)	amongst
as	as (sin)	out of (that)		le	leis (sin)	with (that)
chuig	chuige (sin)	towards (that)		ó	uaidh (sin)	from (that)
de	de (sin)	of (that)		roimh	roimhe (sin)	before (that)
do	dó (sin)	to (that)		trí	tríd (sin)	by means of (that)
fara	fairis (sin)	beside (that)		thar	thart (sin)	beneath (that)
faoi	faoi (sin)	under (that)		um	uime (sin)	around (that)

Fairis sin > freisin (lit. "besides that ") has an extended meaning of also (in Connacht).
In the meaning "also" there is also (in Munster) the word leis (lit.: "with that") and (in Ulster) fosta

A simple ann means "therein" also (more often) "there". It is used with the verb bí in the meaning "there is, there exists":
Tá teach ann = there is a house (lit.: "is a house in-it")
An bhfuil Dia ann? = Is there a God? (lit.: "is God in-it?")

Ann sin, ann seo, ann siúd are mostly written ansin, anseo, ansiúd and have the further meanings:
anseo = here < ann seo = "in-it this"
ansin = there < ann sin = "in-it that" (temporal also: then)
ansiúd = over there < ann siúd = "in-ti there"

The appropriate interrogatives are formed using cé, cad or cá (overview see there):
dó sin = to that, cé dó = why?
faoi sin = under that, cé faoi = under what?, etc.

with derived prepositions

Combined or derived prepositions connnect with nouns in the genitiv or with possessive pronouns.
The acquire an adverbial meaning through the connection with the possessive pronouns of the 3rd person masc. (often + sin/seo/siúd)

examples:

preposition	deutsch	adverb	deutsch	lit.
ar son	because	ar a shon	because of that	"on its welfare"
de bharr	result	dá bharr sin	as a result	"from-its top of that"
i lár	central	ina lár sin	centrally	"in-its middle that"
i ndiaidh	after	ina dhiaidh sin	afterwards	"in-its after that"
le haghaidh	for	lena aghaidh sin	supporting	"with-its face that"

adverbs out of nouns

Remarkable many adverbs are derived from nouns. Often this took place with the help of the preposition i in the form of the modern prefixes a-, i-, an-, in-, is-, that due to their origin as prepositions, are always unstressed (is- = archaic for sa = in the )
The substantial origin is today hardly recognisable, aside from the constant emphasis on the 2nd syllable (the 1st syllable of the noun part).
Similar constructions are also to be found in German and English (often with the preposition zu, to) (comp. e.g.: engl. today, tomorrow, dt. zutage, zuhause).

Through a change in the (historical) dative to accusative forms (comp. istigh, isteach) word pairs with a shifted meaning occur (drinnen, herein).

examples
inné = yesterdy < i ndé = "in a day"
inniu = today< i ndiu = "in a day"
amuigh = outside< i muigh (i maigh) = "in a field"
amach = out< i mach = "in a field"
istigh = inside< is tigh (sa tigh) = "in the house"
isteach = inside< is teach (sa teach) = "into the house"
amárach = tomorrow< i mbárach = "in a morning"
anuraidh = last year< i n-uraidh = "in last year"
anocht = tonight< i nocht = "in a night"

In adverbs, with the help of other prepositions, one can mostly still recognize the nouns: ar uaireanta = sometimes, etc.

adverbs out of weekdays

These adverbs are in German and English more used as normal nouns of time periods ("On Monday, I go to school"). The adverbs (Mondays = every Monday = gach Luan etc.) are nouns in Irish.

The adverbs are formed with Dé (archaic for day). They are always written capitalized. (Déardaoin always keeps its Dé)

Usage, comp.:
an Luan = the Monday
Dé Luain = on Monday, this Monday
Dé Luain seo caite = last Monday
Dé Luain seo chugainn = next Monday
gach Luan = every Monday, Mondays
ó Luan go Satharn = von Monday bis Saturday

adjectives/adverbs out of numeral words

The last column of the table ist only to be used as an adjective. Instead of tréaga, séaga, seachta also tréfhillte, séfhillte, seachtfhillte.
Further formations of similar adjectives with-chodach (ochtchodach = eightfold).

[ 1 ]
suas and amach mean extended also: completely, fully
e.g.: Tá mé caite amach = I am completely out. Amach is amach = through and through