We use the book "C*-algebras and operator theory" by Gerard J. Murphy, Academic Press, ISBN 0-12-511360-9.
Final syllabus (pensum for the exam): from Murphy's book, chapter 2 (sections 2.1 and 2.3), chapter 3 (except section 3.5), chapter 4 (section 4.1 up to Thm 4.1.12, section 4.2 from 4.2.5 to 4.2.8, section 4.3 from 4.3.1 to 4.3.3, section 4.4 up to Thm 4.4.3), chapter 5 (up to 5.1.13).