In the US and several other countries, второе воскресенье мая (“the second Sunday in May”) is День матери, Mother’s Day. In Russia, moms have usually been honored on Восьмое марта (“the 8th of March,” aka “International Women’s Day”), though technically there is a День матери in late November.

Obviously, we can’t say much по-русски on the subject of motherhood without knowing the basic word мать. We can define it in Russian as женщина, по отношению к её детям (“a woman in relation to her children”) — or in zoological contexts, самка по отношению к её детёнышам (“a female animal in relation to her offspring.”)

For beginners, let’s take a look at the highly unusual declension of мать. It has the same case endings as any typical feminine noun ending in -ь, such as мышь (“mouse”) or кость (“bone”) or вещь (“thing”). But what makes this one unusual is that a -ер- pops in «откуда ни возьмись», “from out of nowhere“, except in the nominative and accusative singular. Oh, and just to make your life harder, the stress is sometimes on the stem, and sometimes on the case ending. Here’s the complete declension, with the end-stressed forms highlighted in red:

мать (“mother”)
	sing.	pl.
nominative	мать	матери
genitive	матери	матерей
dative	матери	матерям
accusative	мать	матерей
instrumental	матерью	матерями
prepositional	матери	матерях

For beginners, there are no easy mnemonic tricks to learning exceptional words like this one; you just have to recite the forms until they stick in your head. Or, as the famous rhyming proverb goes, «Повторение — мать учения!» (“Repetition is the mother of learning.”) But don’t be a slacker about it, because as a famous, non-rhyming proverb goes: «Лень — мать всех пороков!» (“Laziness is the mother of all vices/defects!”).

Memorizing the declension of мать is actually a 2-for-1 deal, because the word дочь (“daughter”) follows exactly the same pattern of endings and stress-shifts. (So, for example, it’s дочери in the dative singular, but дочерям in the dative plural.) But these two words are, as far as I know, totally unique — if there are any other nouns in the Russian language with this pattern, they’re much too obscure for non-natives to worry about.

From мать we get such derivatives as the adjective материнский (“maternal; motherly; belonging to mom”), and also an abstract noun:

Материнство — вторая по древности профессия
“Motherhood — the second-oldest profession.”
(title of a book by American humorist Erma Bombeck)

As you may know, affectionate diminutives are used much more often in Russian than in English — so from дочь we get дочка, which implies “one’s darling daughter”. HOWEVER, the seemingly logical diminutive матка is generally not used in regard to human mothers, at least not in standard educated Russian. Instead, матка usually means the “womb/uterus” of any female mammal, including humans. (In certain contexts it can refer to non-human mothers, as in пчелиная матка, “queen bee”.)

So if you need an affectionate diminutive for a human mother, you can use мама (“mom”) instead. Мама has its own diminutives — most often мамочка, though маменька may be found in old literature.

Мамочка, мы больше не будем!
“Mommy, we won’t do it anymore!”
(said by children caught doing something bad)

And a grown man who has never cut the пуповина (“umbilical cord”) and who постоянно «держится за юбку» мамы (“perpetually clings to mom’s skirt”) may be called a маменькин сынок (“mama’s boy”).

Of course, there are other nouns that describe women in maternal or mother-like relationships. You may already know бабушка, “grandmother.” And a родная мать (“birth/biological mother”) can be contrasted with a приёмная мать, “mother by adoption”. (Note that приёмный can apply to either the parents or the children in a adoptive relationship — thus, приёмный сын, “adopted son”).

Other motherly relationships can be established by marriage. So, for instance, you’ve got мачеха, “stepmother,” whose reputation in jokes and fairytales is almost as bad as that of the тёща (“the groom’s mother-in-law”). For some unfair reason, the свекровь (“bride’s mother-in-law”) doesn’t come in for nearly as much cultural abuse! And a крёстная мать is your own godmother, but shouldn’t be confused with кума, who is either the godmother of your children, or the mother of your godchildren. (In other words, the mother and the godmother are кумы to each other.)

And now let’s consider a few verbs relating to материнство…

«А мама, откуда берутся дети?»
“Mom, where do babies come from?”

Perhaps the most central and defining verb is:

родить (кого/что) (“to give birth to; to bear” perf.)
Past	родил, родила, родило, родили
	sing.	pl.
1st	рожу	родим
2nd	родишь	родите
3rd	родит	родят
Imperative	роди(те)!
Past Passive Participle	рождённый

(I’ve included the past passive participle in the table because, going by the general rules for PPP formation, you would logically predict it to be рожённый, not рождённый!)

So, for example, there’s the expression как мать родила, literally “as mother gave birth (to you)”, which is a synonym for голый, “naked”:

На этом пляже все ходят «как мать родила».
At this beach, everyone walks around stark raving nude.

The corresponding imperfective for родить is, usually, рождать, which has no stress shifts or consonant mutations to worry about. Thus, in the present it’s я рождаю, ты рождаешь…; and in the past it’s рождал, рождала. In colloquial contexts, you may also come across the imperfective рожать — which conjugates just like рождать, minus the -д-. Attaching the reflexive ending -ся to рождать/родить gives the meaning “to be born”:

В нашем городе, с две тысячи девятого года ни один ребёнок не рождается с ВИЧ.
In our city, not one child has been born with HIV since 2009.

Incidentally, рождать/родить will generally work for dogs, elephants, and other mammals besides humans. But if you’re talking about egg-laying creatures, you can instead use выводить/вывести, “to hatch out (offspring)”:

Матка Чужих вывела двадцать три личинки.
The queen-alien hatched 23 larvae.

But there’s more to motherhood (or there should be!) than just makin’ babies. Children also need a proper воспитание, “upbringing.” (This word can sometimes be a synonym for образование, “education,” except that воспитание emphasizes moral and civic education more than academic skills like reading and arithmetic.)

The corresponding verb is воспитывать/воспитать (“to raise, bring up, morally educate”) — related to питать, “to feed/nourish,” and пища, “food.” Both the imperfective and perfective have predictable -аю, -аешь, -ает conjugations without any stress shifts:

Как правильно воспитать ребёнка?
How does one correctly bring up a child?

Sometimes the verb is used in the construction воспитать что-нибудь в кого-нибудь, “to instill/inculcate something in someone”:

«Наши мамы воспитали в нас самостоятельность и любовь к человечеству» — сказали земляне.
“Our moms instilled in us self-reliance and a love for humanity,” said the Earthlings.
«А наша мама воспитала в нас самостоятельность и влечение к ЧЕЛОВЕЧИНЕ» — ответили Чужие.
“And our mom instilled in us self-reliance and a craving for «long-pig»,” replied the space-aliens.

Last but not least, mothers care for their children. “Take care of” or “care for” can be expressed by the verb (по)заботиться о ком/чём (prepositional) — note that the noun забота means “concern”. The conjugation of this one is я забочусь, ты заботишься, with a consonant mutation in the 1st-person singular, but no stress shift:

Мама, спасибо за то, что ты всегда заботишься обо мне!
Mom, thanks for the fact that you’re always concerned about me!

P.S. If you’re talking about houseplants or pets, the imperfective verb ухаживать за кем/чем (instrumental) can also mean “to take care of,” but reader Fitzmat recommends that in the context of humans, you’d typically use this verb for someone “taking care of” a sick child or adult.