I would like to express my acknowledgment to faculty, postdocs, students, visitors in the Department of Animal and Dairy Science at the University of Georgia, and the users and the developers of the software for their questions about the BLUPF90 programs, which encourage me to decide to write this note.

While I was writing the initial version of this tutorial, Andrés Legarra reviewed the draft and made a massive amount of corrections and improvements on it. He also wrote sections Renumbering the data without RENUMF90, EM-REML algorithm, Likelihood ratio test, and several other subsections.

I thank Ignacy Misztal for his development of the wonderful software, Shogo Tsuruta, Ignacio Aguilar, and Andrés Legarra for the discussion on their implementation of algorithms in BLUPF90, Luis Varona, Benoit Auvray, Tomasz Strabel, Tom Druet, Deuk-Hwan Lee, Jesus Arango, Juan Pablo Sánchez, Miguel Pérez-Enciso, and François Guillaume for their contribution to the software development, Daniela Lourenco for the discussion on the design of BLUPF90 programs and her useful comments to improve this tutorial, and Ivan Pocrnić for his comments on the draft of this tutorial.

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