Is King David the only author of the Holy Book of Psalms, or are there other authors? If there are, which psalms did they write?

King David is not the only composer of the Holy Book of Psalms. Actually there are only 73 of the 150 (151 in the Septuagint) that are clearly attributed to King David. Others include contemporaries of David's whom he had placed in charge of worship in Jerusalem like Ethan, Heman, and Asaph. Moses & King Solomon also wrote psalms.

King David wrote (Ps 3-9;11,12-32,34-41,51-65,68-70,86,101,103,108-110,122,124,131-133,138,140-145). Moses wrote the Holy Book of Ps 90, Asaph (1 Chron 16:4-5) (Ps 50,73-83), Levites such as the Sons of Korah (Ps 42,44-49,84,85,87) Heman (Ps 88) Ethan (Ps 89), Solomon (Ps 72,127). The composers of many of the Psalms remain anonymous.

Although not all Psalms were authored by King David, the whole book was attributed to him under the general consensus that David was without doubt the anointed of God and the ideal king who presented the psalms as a way of worship for the entire congregation.

This Q&A was found on Archangel Michael & St Bishoy Coptic Orthodox Church : http://www.stbishoy.org.au/modules/smartfaq/faq.php?faqid=80