While English and Icelandic share similar origins as Germanic languages, the differences between them are stark. Under the influence of Norman French, English dropped nearly all of its declensional endings save for -s/z for plurals and possessives (while written differently, they're indistinguishable in spoken language). In contrast, Icelandic is absolutely brimming with them.

Noun Quality

Several aspects of a noun that English indicates either through word order or context are indicated in Icelandic by inflectional endings. This allows the word order of Icelandic to be far more flexible than that of English. It also changes the pronunciation. Minor differences in inflectional endings have to be enunciated, even if the syllable in which they are contained is not stressed.

Gender

All Indo-European languages, including English, possess a concept of grammatical gender. English is unique in that gender in the standard dialect is assigned logically. Male persons and creatures are masculine, female persons and creatures are feminine, inanimate objects are neuter. The majority of other Indo-European languages, Icelandic included, eschew delegation according to biological gender and assign gender to inanimate things randomly. There are three genders in Icelandic; masculine, feminine, and neuter. Unlike German, one can usually deduce the gender of a word just by looking at its Nominative singular form. But unlike Spanish, the cues are much more complicated. While an exhaustive list is impossible, the majority of words will have an ending among those listed below.

Masculine

Exclusively masculine:

  • -aður
  • -uður
  • -ingur
  • -ungur
  • -undur
  • -dómur
  • -leikur
  • -háttur
  • -skapur
  • -all
  • -ill
  • -ull
  • -ann
  • -inn
  • -ingi
  • -ungi
  • -ji
Exclusively masculine with minor exceptions:
  • -ar (sumar, n. - summer)
  • -ir (móðir - mother, dóttir - daughter, systir - sister, all feminine)
  • -ari (altari, n.)
Usually masculine:
  • -ur
  • -andi

Feminine

Exclusively feminine:

  • -ing
  • -úð
  • -un
  • -an
  • -yn
  • -und
  • -urð
  • -semd
  • -ja
  • -ynja
  • -sla
  • átta
  • -usta
  • -ka
  • -ska
  • -eskja
  • -fraeði
Usually feminine:
  • -a

Neuter

Exclusively neuter:

  • -al
  • -að
  • -ald
  • -an
  • -ang
  • -arn
  • -in
  • -erni
  • -elsi
  • -indi
  • -gin
  • -orð

Number

In this respect Icelandic is very similar to English. There are two numbers, singular and plural. They are distinguished under the same conditions as English. Inflectional endings usually distinguish number. When they do not, the situation is analogous to the English singular-plural pair sheep/sheep: a rare, old word that often has collective connotations in any case.

Case

This should be familiar to those with knowledge of Latin, Sanskrit, German, or many of the Slavic languages. Icelandic distinguishes four cases: Nominative, Accusative, Dative, and Genitive. Among conjugational pardigms, the genitive singular, nominative plural, and accusative plural show the greatest varience.

Nominative
The Nominative case marks the subject of a verb phrase. As an example in English, he is a pronoun in the Nominative case.

Accusative
The Accusative case is also fairly simple. It marks the direct object of a verb phrase. Him is a pronoun in the Accusative case. In verbs that take two direct objects, like in the sentence, The town elected him mayor, both objects are in the accusative. Certain impersonal verbs have an accusative which functionally acts as their subject, the true subject left off. For example, hana vantar peninga (literally her it.needs money, actually she needs money). When used with prepositions or adverbs, it gives a sense of motion. For example, í akurinn with akur in the Accusative means into the field, whereas í akurinum with akur in the Dative means in the field.

Dative
Speaking of... the Dative case marks the indirect object of a verb phrase. An indirect object is not directly acted upon by the verb, but is rather a benificiary of the action. For instance, in Kjartan gaf henni peninga (Kjartan gave her money), the pronoun hún is in the Accusative. The sentence could also be written Kjartan gaf peninga henni (Kjartan gave money to her). Since the information is contained within the inflection, there's no need to add a preposition as in English. Icelandic word order is more flexible, so one is able to emphasize certain aspects of the sentence while still retaining coherency. Of note is that subjects of passive verbs remain in the Dative, unlike English. Henni var gifen peninga af Kjartan (She was given money by Kjartan). The dative also functions as the subject of certain verbs. These verbs usually denote mental states, responsibility, quick movement, instrumental use, and deprivation. Adjectives and adverbs with respect to an object may be juxtaposed with the object in Dative, but this is more literary language. In colloquial Icelandic a prepositional phrase is preferred. Finally, the Dative is often used with prepositions, denoting a sense of position instead of movement. See the í akurinum example above.

Genitive
The last case, the Genitive, denotes possession. It substitutes for both the English Genitive inflection, 's, and the preposition of. Indeed the Icelandic inflection is often exactly the same as in English. There are significant differences, however. In English we tend to separate active possession from passive possession, the former being indicated by inflectional while the latter by prepositional phrase. Icelandic makes no such distinction, using the Genitive in both cases. The word order is also different, Icelandic usually has the possessor follow the thing it possesses. This holds for possessive pronouns as well. Like the Dative case, the Genitive stands as the direct object of certain verbs. Also like the Dative, the Genitive is used in prepositional phrases, generally with a meaning of relative location or abstract association.

Declension

Icelandic declension is not regular. At all. It does, however, follow patterns, some of which are more common than others. One can find a parallel in English verbs. The majority follow the pattern of love, loved, loved, but there are also irregular groups like swim, swam, swum or wear, wore, wore. It's the vast amount of these patterns in Icelandic that causes problems. As an illustration, Latin, a famously declension-happy language, has twenty declension patterns including irregular nouns. Icelandic has seventy-three. So much for that. One item of solace is that in all patterns the -um or -m of plural Dative and the -a of plural Genitive remains the same.

Noun declensions are sorted into two broad types, called strong and weak. Just like with strong and weak verbs in English, the strong category contains all the irregulars. These two categories are further divided among the three genders. Finally, they are sorted into classes according to their Nominative plural and Genitive singular case endings.

Strong Declension

The strong declension is characterized by by a Genitive singular that always ends in a consonant, either -s or -ar. It also exhibits far more variance than the weak declension, which is why it is called strong. Words within it tend to buck regular declension patterns. Besides case ending variation, there are also mutations to the root word within certain cases. This is called umlaut, and came about because certain vowels following a syllable caused a sound change to come about in that syllable.

Masculine

Class 1
Marked by a Genitive singular of -s and Nominative plural of -ar. Singular charts come above plural charts, and an example word of each paradigm within the class is labeled and declined.
      Common    Umlaut   Monosyllabic   Mono/Bisyllabic
Nom.| pískur | hattur | skór        | karl
Acc.| písk   | hatt   | skó         | karl
Dat.| píski  | hatti  | skó         | karl
Gen.| písks  | hatts  | skós        | karls
Nom.| pískar | hattar | skóar       | karlar
Acc.| píska  | hatta  | skóa        | karla
Dat.| pískum | höttum | skóum       | karlum 
Gen.| píska  | hatta  | skóa        | karla

      Monosyllabic  Suffixed   
Nom.| bíll       | jökull  | 
Acc.| bíl        | jökul   |
Dat.| bíli       | jökli   |
Gen.| bíls       | jökuls  |
Nom.| bílar      | jöklar  |
Acc.| bíla       | jökla   |
Dat.| bílum      | jöklum  |
Gen.| bíla       | jökla   |
Class 2
Marked by Genitive singular of -s and Nominative plural of -ar. Final stop words of Class 2 may sometimes have a Genitive singular of -ar to be memorized. Many words in this class have no -ur in the Nominative singular, such as the all-important guð (God).
      Uncommon  Umlaut   Final Stop
Nom.| smiður | dalur  | leikur
Acc.| smið   | dal    | leik
Dat.| smið   | dal    | leik
Gen.| smiðs  | dals   | leiks
Nom.| smiðir | dalir  | leikir
Acc.| smiði  | dali   | leiki
Dat.| smiðum | dölum  | leikjum
Gen.| smiða  | dala   | leikja
Class 3
Marked by Genitive singular of -ar and Nominative plural of -ir.
      Common   Umlaut
Nom.| hlutur | spónn
Acc.| hlut   | spón
Dat.| hlut   | spæni
Gen.| hlutar | spóns
Nom.| hlutir | spænir
Acc.| hluti  | spæni
Dat.| hlutum | spónum
Gen.| hluta  | spóna
Class 4
Inconsistent Genitive, Nominative plural of -ur. Mostly a unique class for common words, which sadistically undergo very strange and inconsistent umlauts during declension. The six normal ones are listed without labels, any others in this class have fallen out of even literary usage.
Nom.| bróðir  | faðir   | fingur  | fótur | vetur  | maður
Acc.| bróður  | föður   | fingur  | fót   | vetur  | mann
Dat.| bróður  | föður   | fingri  | fæti  | vetri  | manni
Gen.| bróðurs | föðurs  | fingurs | fótar | vetrar | manns
Nom.| bræður  | feður   | fingur  | fætur | vetur  | menn
Acc.| bræður  | feður   | fingur  | fætur | vetur  | menn
Dat.| bræðrum | feðrum  | fingrum | fótum | vetrum | mönnum
Gen.| bræðra  | feðra   | fingra  | fóta  | vetra  | manna

Feminine

Class 1
Marked by Genitive singular of -ar or -r and Nominative plural of -ar. This class holds the trend-subverting feminine nouns that end in -ur for their Nominative singular.
      Common   Suffixed    False      Stem
Nom.| kinn   | hreyfing  | lifur | stó
Acc.| kinn   | hreyfingu | lifur | stó
Dat.| kinn   | hreyfingu | lifur | stó
Gen.| kinnar | hreyfingar| lifar | stór
Nom.| kinnar | hreyfingar| lifar | stór
Acc.| kinnar | hreyfingar| lifar | stór
Dat.| kinnum | hreyfingum| lifum | stóm
Gen.| kinna  | hreyfinga | lifa  | stóa
Class 2
Marked by Genitive singular of -ar and Nominative plural of -ir. This class is extremely common for feminine nouns. The infixed and umlauted category can sometimes coincide in one word, in which case two of its syllables will change in vowel. A word of that sort is declined in the infixed category to illustrate the dual change.
      Common   Umlaut   Suffixed
Nom.| sveit   | sök   | pöntun
Acc.| sveit   | sök   | pöntun
Dat.| sveit   | sök   | pöntun
Gen.| sveitar | sakar | pöntunar
Nom.| sveitir | sakir | pantanir
Acc.| sveitir | sakir | pantanir
Dat.| sveitum | sökum | pöntunum
Gen.| sveita  | saka  | pantana
Class 3
Marked by a Genitive singular of -ar, -ur, or -r and a Nominative plural of -ur or -r. There are only a few words in this class, and they're all frustratingly irregular. To explain the class thoroughly would be to decline every word in it. Thus it is better just to memorize the declensions of Class 3 feminine words, especially since they're infuriatingly common words like bók (book), kýr (cow), and móðir (mother).

Neuter

Only one class in this gender, marked by a Genitive singular and no ending for the Nominative plural.
      Common   Umlaut    Drop
Nom.| líf   | land    | sumar
Acc.| líf   | land    | sumar
Dat.| lífi  | landi   | sumri
Gen.| lífs  | lands   | sumars
Nom.| líf   | lönd    | sumur
Acc.| líf   | lönd    | sumur
Dat.| lífum | löndum  | sumrum
Gen.| lífa  | landa   | sumra

Weak Declension

All nouns of the weak declension have singular endings in a short vowel: -i, -a, or -u. While there is far less variance in this declension, there are still a few subdivided classes.

Masculine

Class 1
Marked by a Genitive singular of -a and a Nominative plural of -ar. There are once again two common umlaut transformations in this class, both of which sometimes occur in the same word such as in the example with bakari.
      Common    Umlaut   Infixed
Nom.| sviði  | vani   | bakari
Acc.| sviða  | vana   | bakara
Dat.| sviða  | vana   | bakara
Gen.| sviða  | vana   | bakara
Nom.| sviðar | vanar  | bakarar
Acc.| sviða  | vana   | bakara
Dat.| sviðum | vönum  | bökurum
Gen.| sviða  | vana   | bakara
Class 2
Marked by a Genitive singular of -a and a Nominative plural of -ur. These are universally present participles of verbs which have become nouns. They are few and function exactly like Class 1 except with -ur for the plural Nominative and Accusative. Umlaut is sometimes undergone for the entire plural declension because of contraction from the original noun.

Nom.| bóndi
Acc.| bónda
Dat.| bónda
Gen.| bónda
Nom.| bændur
Acc.| bændur
Dat.| bændum
Gen.| bænda

Feminine

Class 1
Marked by a singular Genitive of -u and a Nominative plural of -ur. Divided into two types, those with an -n infix in the Genitive plural and those without. Normal umlaut of the a-stem occurs in both, as illustrated throughout nearly every other declensional table above.
      Infixed  Non-Infixed
Nom.| saga   | lilja 
Acc.| sögu   | lilju
Dat.| sögu   | lilju
Gen.| sögu   | lilju
Nom.| sögur  | liljur
Acc.| sögur  | liljur
Dat.| sögum  | liljum
Gen.| sagna  | lilja
Class 2
Marked by a singular Genitive of -i and no plural. Its declension is... er... rather simple. This class is composed almost entirely of abstract nouns formed from adjectives, for which a plural would not make cognitive sense. There are also a few irregular nouns with plurals in need of memorization.

Nom.| gleði
Acc.| gleði
Dat.| gleði
Gen.| gleði

Neuter

Only a few words which decline regularly, mostly body parts. The -n- infix of weak feminine nouns is observed universally.
     Common   Umlaut
Nom.| lunga  | hjarta
Acc.| lunga  | hjarta
Dat.| lunga  | hjarta
Gen.| lunga  | hjarta
Nom.| lungu  | hjörtu
Acc.| lungu  | hjörtu
Dat.| lungum | hjörtum
Gen.| lungna | hjartna

Definite Article

Icelandic possesses a definite article like the English the, although no indefinite article. It is used in exactly the same manner, but somewhat less commonly than in English. It is not used with many collective nouns, occupation nouns, place names that could be proper nouns, and general state nouns like bóndi (farmer) and stúlkur (girls). Definite articles decline just like nouns according to gender, number, and case. They can either precede the noun as in English, or be added as a suffix to the noun.

Free Definite Article

The free definite article can only be used if an adjective separates it from the noun it modifies. For example, one can write hinn góði maður, but not hinn maður. Even then, the free definite article is only used in literary style, where it is also sometimes written without an h-. Colloquial speech nearly always suffixes the definite article. The free definite article declines thus:
      Masc     Fem      Neut
Nom.| hinn   | hin    | hið
Acc.| hinn   | hina   | hið
Dat.| hinum  | hinni  | hinu
Gen.| hins   | hinnar | hins
Nom.| hinir  | hinar  | hin
Acc.| hina   | hinar  | hin
Dat.| hinum  | hinum  | hinum
Gen.| hinna  | hinna  | hinna

Suffixed Definite Article

The suffixed definite article functions somewhat like a separate system of declension. As it is attached to the end of words in each case, it often changes the ending that comes before it. The variations of the suffixed definite article are, thankfully, far fewer than those of the actual declensions. Certain changes are common to all suffixed nouns. The -m of the Dative plural is always lost. The -a of the Genitive plural is lost if it would be preceded by an accented vowel. False masculine nouns ending in -ur lose the -u- in all suffixes. The -i- of the suffix itself is lost in nouns of the weak declension and after the stem vowel .

Masculine

     S. Class 1   S. Class 2    Monosyllabic  Weak
Nom.| pískurinn | smiðurinn  | skórinn     | vaninn
Acc.| pískinn   | smiðinn    | skóinn      | vanann
Dat.| pískinum  | smiðnum    | skónum      | vananum
Gen.| písksins  | smiðarins  | skóins      | vanans
Nom.| pískarnir | smiðirnir  | skórnir     | vanarnir
Acc.| pískana   | smiðina    | skóna       | vanana
Dat.| pískunum  | smiðunum   | skónum      | vönunum
Gen.| pískanna  | smiðanna   | skónna      | vananna
Feminine
      Common       Stem       False        Weak
Nom.| kinnin     | stóin    | lifrin     | sagan
Acc.| kinnina    | stóna    | lifrina    | söguna
Dat.| kinninni   | stónni   | lifrinni   | sögunni
Gen.| kinnarinnar| stórinnar| lifrarinnar| sögunnar
Nom.| kinnarnar  | stórnar  | lifrarnar  | sögurnar
Acc.| kinnarnar  | stórnar  | lifrarnar  | sögurnar
Dat.| kinnunum   | stónum   | lifrunum   | sögunum
Gen.| kinnanna   | stónna   | lifranna   | saganna
Neuter
      Common     Stem-É    Drop        Weak
Nom.| landið   | tréð    | sumrið    | lungað
Acc.| landið   | tréð    | sumrið    | lungað
Dat.| landinu  | trénu   | sumrinu   | lunganu
Gen.| landsins | trésins | sumursins | lungans
Nom.| löndin   | trén    | sumrin    | lungun
Acc.| löndin   | trén    | sumrin    | lungun
Dat.| löndunum | trjanum | sumrunum  | lungunum
Gen.| landanna | trjanna | sumranna  | lungnanna

Sources used:

Einarsson, Stefán., Icelandic. Baltimore: The Johns Hopkins University Press, 1945
Neijmann, Daisy L., Colloquial Icelandic. London: Routledge, 2001.