Besides the informal singular form, Turkish has two different forms of the imperative. The second form is used to address multiple persons, and can also be used to formally address a single person, for example if the person is your superior, older than you, or a stranger. It consists of the stem plus a suffix, which depends on the last vowel in this stem.

In total there are three forms to give orders to a person using the imperative form:

The first form is used for addressing a single person informally
The second form is used for addressing a single person politely or multiple people informally
The third form is used mainly in official language for addressing a single person or multiple people very politely

The three forms all have their own grammar:

The first form consists of the verb stem
The second form consists of the verb stem + (y)İn
The third form consists of the verb stem + (y)İnİz

The İ's are written with capital letters above, because they change depending on the last vowel in the stem:

Last vowel in stem	i or e	ı or a	u or o	ü or ö
Suffix	(y)in / (y)iniz	(y)ın / (y)ınız	(y)un / (y)unuz	(y)ün / (y)ünüz

The y is between parentheses here, because it is only present in case the stem ends in a vowel. It acts as a buffer letter to prevent two vowels ending up next to each other.

Beneath you can see some examples of the three forms:

English	First form	Second form	Third form
Come.	Gel.	Gelin.	Geliniz.
Buy tea.	Çay al.	Çay alın.	Çay alınız.
Walk.	Yürü.	Yürüyün.	Yürüyünüz.
Read a book.	(Bir) kitap oku.	(Bir) kitap okuyun.	(Bir) kitap okuyunuz.

The way in which the İ changes between i, ı, u and ü, depending on the preceding vowel, is called the major vowel harmony. Major vowel harmony will recur again and again in the Turkish language and might seem difficult at first, but you will quickly learn to use it with ease.

Breakdown of Geliniz.