Latin Third Declension Nouns

These are divided into several classes:

1. Consonantal stems
1. masculine and feminine
2. neuter
2. i-stems
1. masculine and feminine
2. neuter

Consonantal stems

Basic paradigm

Some examples

1. Masculine and feminine
• anser, anseris. nm., goose.
• canis (or rarely: canes), canis. nm., 1. dog, hound, mutt.  2. subordinate.  3. Sirius, Alpha Canis Majoris, the Dog Star (i.e. the brightest star in the night sky, known also as "the Dog Star" because it is the brightest star in the constellation Canis Major [= the Big Dog]).
• cervix, cervicis. nf., neck.
• custos, custodis. nm., guard.
• feles (or rarely: felis), felis. nf., cat, mouser, marten, ferret, polecat, tomcat.  (Note: English cat, French chat and Italian gatto come from an unrelated second declension noun: catus, -i. nm., 1. wildcat, male cat.  2. catfish.  3. a kind of siege engine.)
• frater, fratris. nm., brother.
• leo, leonis. nm., lion.
• mater, matris. nf., mother.
• miles, militis. nm., soldier.
• mulier, mulieris. nf., woman.
• iuglans, iuglandis. nf., walnut.
• fons, fontis. nm., spring, fountain, origin, source.
• mons, montis. nm., mountain.
• nox, noctis. nf., night.   loc. noctu, by night.
• ops, opis. nf., power, help.
• pars, partis. nf., part, share.
• pater, patris. nm., father.
• plebs (or pleps), plebis. nf., commoners, plebeians, common people, masses, (in George Orwell's 1984) plebs. (Also there is a pre-Augustan fifth declension form plebes, plebei.)
• radix, radicis. nf., root, foot of a mountain, foundation, origin. (math.) root.
• rex, regis. nm., king.
• soror, sororis. nf., sister.
• uxor, uxoris. nf., wife.
• vigil, vigilis. nm., fireman.

Feminine abstract nouns ending in -io(n)

These are formed from perfect passive participles:

<participle stem> + -io

For example:

verb	incanto (1). vt. (to) enchant, cast a spell (on).     (from canto (1). vt. (to) sing, recite.)
passive participle	incantatus
participle stem + ending	incantat- + -io
abstract noun	incantatio. nf. incantation, spell, enchantment.

This was commonly used for word creation in scientific Latin, and I believe it is still in common use in contemporary ecclesiastical Latin. 

Some English neologisms also make use of this form of creation, not always consistently, e.g., verbification (modelled after clarification [from medieval Latin clarifico (1) from Latin clarus + facio, facere, feci, factus] and glorification [from medieval Latin glorifico (1) from Latin gloria + facio, facere, feci, factus]).  Verbification can refer to new word creation in a language, or t can refer to a process of constructing verbs from nouns (for example, "to book a suspect".) 

• aequatio, -ionis. nf., (math.) equation, identity. (from aequo (1). vt. make equal, match.)
• declaratio, -ionis. nf., statement. (from declaro (1). vt., clarify.)
• evolutio, -ionis. nf., unrolling a scroll, reading, (sci.) development, (math.) expansion (e.g. into series or products). (from evolvo, -vêre -vi, -utus. vt., unroll, unfold, spread, expand.)
• fluctuatio, -ionis. nf., wavering, fluctuation. (from fluctuo (1). vt. waver, fluctuate.)
• fractio, -ionis. nf., (math.) fraction. (from frango, -ere, fregi, fractus. vt. smash, shatter, break.)
• functio, -ionis. nf., performance, (math) function. (from fungor, fungi, functus sum. vi. perform.)
• occasio, -ionis. nf., occasion, opportunity.
• incantatio, -ionis. nf., spell, enchantment. (from incantatus, pp. of incanto (1). vt., enchant, cast a spell on.)
• oratio, orationis. nf., speech, language, expression. (from oratus, pp. of oro (1). vt., beg for, plead.)

Masculine nouns of agency ending in -or, -oris

These are formed from perfect passive participles:

<participle stem> + -or

• doctor, -oris, nm., teacher. (from doceo (2ui), vt. teach.)
• gladiator, -oris, nm., gladiator. (from gladius, nm. sword.)
• imperator, -oris, nm., general, commander, emperor. (from impero (1), vt. order, command.)
• monitor, -oris, nm., advisor. (from moneo (2), vt. warn, advise.)
• vector, -oris, nm., rider, passenger. (from veho, vehere, vexi, vectus (3), vt. carry, transport.  The modern mathematical term vector is from the Latin word.  There is also a related Latin verb vecto (1), also transitive, and very similar in meaning -- its past participle vectatus clearly does not give the stem for vector.)

Feminine abstract nouns ending in -tas, -tatis

These are formed from adjectives:

<root> + -(i)tas

• aequalitas, -tatis. nf., equality. (from aequal, adj., equal. from aequus, adj., level, even.)
• fraternitas, -tatis. nf., brotherhood. (from fraternus, adj., brotherly. from frater. nm., brother.)
• libertas, -tatis. nf., freedom. (from liber. adj., freedom.)
• maiestas, -tatis. nf., majesty.
• maioritas, -tatis. nf., majority. (from maior. adj., larger, more important.)

Feminine abstract nouns ending in -tudo(n)

These are formed from adjectives:

<root> + -(i)tudo

• magnitudo, magnitudinis. nf., size, importance, extent. (from magnus. adj., large, important.)
• multitudo, multitudinis. nf., great number, crowd, mob, rabble. (from multus. adj., much, many, large, tedious.)

1. Neuter
• caput, capitis. nn., head.
• cor, cordis. nn., heart.
• genus, generis. nn., gender.
• iter, iteris. nn., road.
• lemma, lemmatis. nn. (Greek), theme, matter or subject for consideration. Math: a subsidiary theorem used primarily to prove a main result, lemma.
• opus, operis. nn., work.
• theorema, theorematis. nn. (Greek), proposition to be proved, theorem.

Neuter nouns ending in -men, -minis

(These don't appear to have any common means of formation, but appearances are often deceiving.  If you know details of how these are formed, please share your knowledge with me.)

• crimen, -minis. nn., accusation, charge, guilt, crime. (source [not cause!] of English crime, criminal.)
• flumen, -minis. nn., flow, river, stream. (probably related to fluo, fluere, fluxi, fluctus. flow, emanate, proceed from.)
• limen, -minis. nn., threshold, doorway, border. (source of English subliminal, eliminate.)
• nomen, -minis. nn., name, noun.
• pronomen, -minis. nn., pronoun.
• stamen, -minis. nn., thread.

i-stem

Basic paradigm

Some examples

• animal, animalis. nn., animal.
• hostis, hostis. nm., enemy.
• mare, maris. nn., sea.