Wool might be divided in three categories, considering the cutting season:
a) Spring-cut wool
b) Autumn-cut wool

Considering the quality and color:
1- fresh wool
2- body-washed wool
3- single-washed wool
4- cut wool
5- First-cut wool
6- raw wool
7- self-colored wool
8- tanning wool
9- mixed wool
10- hand-washed wool
11- dyed wool
12- two layer twisted wool
13- live wool
14- Washed wool
15- root out wool
16- old wool
17- belly washed wool
18- machine-washed wool
19- carded wool
20- dead wool
21- mixed non-scoured wool
22- non-scoured wool
23- semi-washed wool
24- uniform wool

From the viewpoint of quality:
1- natural wool
2- artificial wool

It is an aspect in quality of wool that best and most wanted wool, is the one with compiled and blended filaments. Those are quite strong, while having a silky sparkle. Wool being cut from the leg or under belly of sheep, may not be advised.