Arabic script is rich and varied, featuring several calligraphic styles used historically and contemporarily. Here are some of the prominent scripts:
Naskh: This is one of the most popular scripts in the Arab world. It is characterized by its clarity and readability, making it ideal for use in writing books and newspapers source.
Kufi: Known for its angular and square-shaped letters, the Kufi script was widely used in early Islamic manuscripts. It is a decorative form often used in architecture and coin design source.
Diwani: This script is known for its intricate and ornate style, often used in official documents and artistic expressions.
Thuluth: Distinguished by its large, cursive letters, Thuluth script is commonly used in architectural inscriptions.
Ruq'ah: Often used in everyday handwriting, Ruq'ah is simple and easy to write, making it an efficient script for personal notes and correspondence.
You can explore more about these styles and their applications on Wikipedia and other resources.
Images of these scripts can be seen here: