по

across, on, along, down, up, all over, (all) around+ dative — used broadly to indicate action, typically involving movement, across a surface or across several things in a generally flat plane

for, on, about, in, of+ dative — used to indicate the object/field/topic that something applies to; or translated with an attributive noun followed by a noun

• Я знаю её по имени.

  I know her by name.

  Tatoeba · marafon · CC BY 2.0 FR

• Я знал их всех по именам.

  I knew them all by name.

  Tatoeba · marafon · CC BY 2.0 FR

according to, from, by+ dative — used to indicate accordance with, adherence to or judgement based on something

due to, on account of, out of, from, by+ dative — used to indicate the reason for something, typically undesired/undesirable (see usage notes on из-за (iz-za))

on, in (the), every (or translated with a plural noun)+ dative — used with time (usually times of day or days of the week) to indicate regular repetition

• У меня нет мнения по этому вопросу.

  I have no opinion on this topic.

  Tatoeba · marafon · CC BY 2.0 FR

• Я люблю говорить по телефону.

  I like to talk on the phone.

  Tatoeba · gregoryguy · CC BY 2.0 FR

and numbers ending in these words)+ dative — used with numbers when there is distribution among multiple objects or repetition across multiple instances in time (dative case is used with the numbers one, a thousand, a million, a billion, a trillion etc

or numbers ending in these words)+ accusative — used with numbers when there is distribution among multiple objects or repetition across multiple instances in time (inanimate accusative case is used with numbers other than one, a thousand, a million, a billion, a trillion etc

Used to indicate something serving as the boundary of the extent of some action+ accusative

(immediately) after, upon, on+ prepositional — Used to indicate a temporal or spatial boundary

• После школы Том посещает дополнительные занятия по математике.

  Tom attends maths enrichment classes after school.

  Tatoeba · Selena777 · CC BY 2.0 FR

to the liking of+ prepositionalrare