Third Declension

The third declension is probably the most difficult declension in Latin for several reasons. For one thing, third declension nouns can be all three genders (masculine, feminine, or neuter) so you have to memorize the gender along with the word and meaning. For another thing, the nominative singular, the most typical form of a noun and the form under which one looks it up in a dictionary, is often strikingly different from all other forms of the noun. In addition there is a special subclass of third declension nouns called "i-stems" which differ from other third declension nouns only in spelling (and hence pronunciation because Latin is phonographically isomorphic) but it can be difficult to tell whether a certain noun is an i-stem and if you get it wrong everyone will laugh at you and call you an asinus. But once you get past those, the third declension isn't so bad.

A Latin noun is in the third declension if and only if its genitive singular ends in -is. If you take off the -is from the genitive singular you are left with the stem, which is the basis for all the other forms except the nominative singular (oh, and the accusative singular for neuters, but we'll get to that later), which can be anything it wants to be. So without further ado, here is the paradigm for third declension nouns, using "rex" (stem "reg-", meaning "king", gender masculine) as an example (the vocative is always identical to the nominative):

case        singular   plural
nominative: rex        reges
accusative: regem      reges
genitive:   regis      regum
dative:     regi       regibus
ablative:   rege       regibus

Neuters

Neuters of all declensions in Latin (and in Classical Greek) follow two of their own rules which override the normal rules of the declension:

1. The nominative and accusative are always identical.
2. The nominative and accusative plural always end in "-a".

Thus the paradigm for "litus" (stem "litor-", meaning "shore", gender neuter) is:

case        singular   plural
nominative: litus      litora
accusative: litus      litora
genitive:   litoris    litorum
dative:     litori     litoribus
ablative:   litore     litoribus

And that's all there is to neuters!

I-stems

Ah, the dreaded i-stem. I-stems work differently for sexed and for neuter nouns; let's do neuters first. A neuter noun is an I-stem if and only if its nominative singular ends in "-ar", "-al", or "-e". This does nothing but affect the spelling by adding an extra "i" in certain places. Here's a paradigm of "mare" (stem "mar-", meaning "sea", gender neuter) with the extra i's in bold:

case        singular   plural
nominative: mare       maria
accusative: mare       maria
genitive:   maris      marium
dative:     mari       maribus
ablative:   mari       maribus

Masculine and feminine nouns are affected even less by being i-stems (the only change is in the genitive plural) but it is more difficult to determine whether they are i-stems. A sexed noun is an i-stem only if:

1. its nominative singular both ends in "-es" or "-is" and has the same number of syllables as the genitive singular (Parasyllabic Rule)
2. its nominative singular ends in "-s" or "-x" and its stem ends in two consonants.

It would be superfluous to give a paradigm because they only differ from non-i-stems in the presence of a single letter: the genitive plural is "-ium" instead of "-um". The three exceptions to these rules are "iuuenis", "senex", and "canis", which all past the test for i-stems even though they are not. Their genitive plurals are "iuuenum", "senum", and "canum", respectively.

N.B.: Adjectives of the third declension, which normally decline exactly like nouns, are almost always i-stems and their ablative singulars end in "-i" instead of "-e", the normal ending for sexed nouns.

There, now go impress someone with your awesome knowledge of Latin!

Paradigms checked against Oxford Latin Course.