Step 1: Background of Sikh scriptures.
The Adi Granth Sahib is the central scripture of Sikhism, containing the hymns and teachings of Sikh Gurus as well as saints of other traditions.
Step 2: Compilation.
Guru Arjan Dev, the fifth Sikh Guru, undertook the task of compiling the Adi Granth Sahib around 1604 CE. He collected the hymns of Guru Nanak, the succeeding Gurus, and other saints, and installed the scripture at the Golden Temple (Harmandir Sahib) in Amritsar.
Step 3: Conclusion.
Hence, the compilation of the Adi Granth Sahib was done by Guru Arjan Dev.
\[
\boxed{\text{Guru Arjan Dev}}
\]