The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv Sissel Grønmo, Mary Lindquist, Alka Arora) and Chapter 2 (Lee R. Jones, Gerald Wheeler, Victoria A. S. Centurino) present the TIMSS Advanced 2015 Mathematics Framework and the TIMSS Advanced 2015 Physics Framework, respectively, describing in some detail the major content and cognitive domains in advanced mathematics and physics to be tested at the final year of secondary school. The content domains (algebra, calculus, and geometry in mathematics; and mechanics and thermodynamics, electricity and magnetism, and wave phenomena and atomic/nuclear physics in physics) and the topic areas within the domains are presented, with further elaboration on specific objectives of each topic area. The cognitive domains describing the thinking students should be doing within the advanced mathematics and physics content domains are the same for both subjects, albeit with different levels of emphasis. Chapter 3 (Martin Hooper, Ina V. S. Mullis, Michael O. Martin) contains the TIMSS Advanced 2015 Context Questionnaire Framework, describing the types of schooling situations and factors associated with students' learning in advanced mathematics and physics that will be investigated via the questionnaires completed by students, their teachers, and their school principals as well as via the "TIMSS 2015 Encyclopedia". Finally, Chapter 4 (Michael O. Martin, Ina. V. S. Mullis, Pierre Foy) provides an overview of the TIMSS Advanced 2015 test booklet design, and includes general parameters for item development. The following are appended: (1) Acknowledgements; (2) Example Mathematics Items; and (3) Example Physics Items.