з/із/зі

The preposition з functions in several main ways:

1. Origin (From/Off/Out of): Used with the Genitive case. It indicates moving away from the inside of something, off a surface, or geographical origin (e.g., Я з України - I am from Ukraine). It is the directional counterpart to в/у (in) and на (on). Note: Use з for places and objects, but use від for people (e.g., Я йду від лікаря - I am coming from the doctor, not з лікаря).
2. Accompaniment and Interaction (With): Used with the Instrumental case. It indicates being together with someone or something (e.g., кава з молоком - coffee with milk). It is also used for mutual interaction, communication, or conflict (e.g., розмовляти з друзями - to talk with friends, битися з ворогом - to fight with the enemy).
3. Material/Contents (Made of): Used with the Genitive case to describe what something is made of or what it contains (e.g., каблучка із золота - ring made of gold).
4. Time (Since/From): Used with the Genitive case to indicate a starting point in time (e.g., з понеділка - since Monday).
5. Cause/Reason: Used with the Genitive case to indicate why something happens (e.g., з радості - out of joy).
6. Field/Subject: Used with the Genitive case to indicate a subject of study or field (e.g., іспит з математики - math exam).
7. Approximation (About): Used with the Accusative case to indicate a rough amount (e.g., з десяток - about ten). The variant зо is the standard variant used directly with the numerals два and три, but can also appear with other numerals (e.g., зо п'ять - about five).
8. Partitive (One of / Some of): Used with the Genitive case to indicate a part of a group (e.g., один з нас - one of us).
9. Manner (How): Used with the Instrumental case to describe how an action is performed (e.g., з радістю - with joy).
10. Target of Emotion/Action: Used with the Genitive case to indicate the target of laughing, mocking, or marveling (e.g., сміятися з - to laugh at, глузувати з - to mock, дивуватися з - to marvel at). Note that дивуватися can also be used with the Dative case without a preposition (e.g., дивуватися комусь/чомусь). Do not use "над" for laughing/mocking.
11. Size Comparison: Used with the Accusative case for size comparisons (e.g., завбільшки з будинок - the size of a house, розміром з кулак - the size of a fist).

Phonetic Variants:

• з: The standard form. It is preferred after a vowel or before a vowel (з Одеси - from Odesa), and before most single consonants when the preceding word ends in a vowel.
• із: Used between two consonants to aid flow, at the beginning of a sentence before a consonant, or before sibilants (с, з, ш, ж, ч, щ, дж, дз) (із саду - from the garden, із жабою - with a frog).
• зі: Used before words starting with a cluster of consonants, especially if the first is a sibilant (с, з, ш, ж, ч, щ, ц) or in specific clusters like мн, лв, зв (зі школи - from school, зі столу - from the table). Note that із and зі can sometimes be interchangeable before consonant clusters starting with a sibilant. It is always used with мною (зі мною - with me).
• зо: A phonetic variant used for approximation with numerals like два, три, and others (зо дві години - about two hours, зо п'ять - about five), and with the pronoun мною (зо мною - with me).