You can link more than two nouns together in a chain. All the middle nouns end in Kasra (Majroor). Only the LAST noun can take AL.
كِتَابُ مُعَلِّمِ الْمَدْرَسَةِ
Kitaabu mu'allimi al-madrasati
The book of the teacher of the school
1st Noun (Mudhaf)
كِتَابُ
No Tanween. No AL. Damma (Marfoo').
2nd Noun (Middle)
مُعَلِّمِ
No Tanween. No AL. Kasra (Majroor).
3rd Noun (Last — Mudhaf Ilayh)
الْمَدْرَسَةِ
Can take AL. Kasra (Majroor).