The PHD Thesis entitled Perception, transmission and function of science in middle Byzantine era and the Quadrivium of 1008 has as its objective a presentation, as clearly as possible, of the scientific researches and of the general perception of mathematical sciences in the middle Byzantine era, in the area of Byzantine Empire. Thematic axes of the Thesis are the Education on mathematical sciences (a sector that constituted the superior educational stage in Byzantium), the perception of science and the particular text Ευσύνοπτον σύνταγμα εις τας τέσσαρας μαθηματικάς επιστήμας used for the teaching of mathematical sciences. This text, written in 1008 by an unknown writer and been in use until many centuries later, knew wide circulation after the proliferation of typography, considered widely to be the work of Michael Psellus. This text, the first complete handbook on the teaching of the four mathematical sciences, i.e. arithmetic, geometry, music and astronomy, drafted in the Byzantine period, is considered as product of Michael Psellus era, and consequently its study is connected with a number of questions directly or indirectly related to him. But apart from that, the writing of an instructive handbook forms part of the general educational system of a specific society, and is therefore directly related to that society, aiming to correspond to its expectations, needs, its cognitive level and sovereign ideology. Accordingly, it provides information on the cognitive charge that is offered, as well as on what is considered as essential knowledge for the members of the specific society. Finally, the handbook in question can function as a reflection of the perception of science in Byzantium of that era. The Thesis is divided in three chapters, following a general introduction. The introduction brings in an overall presentation of the relevant questions and the determination of the examined period of time and its particularities: middle-Byzantine era, with a focus on the 11th century, time of writing of the handbook.