The mission of university, personnel and the social responsibility of university are discussed in the paper. The mission of university is the first object of reflection. The author argues, that the missions of university is to convert research data into facts and knowledge, the development of social reproduction and the application of knowledge in order to improve the social organisation. The Faculty of philosophy of Vilnius University is analysed through the lenses of the mission. The personnel of university are analyzed in the second part of the paper. The teachers, researchers, administrators, and auxiliary stuff are the personnel of university. The academic freedom and responsibility is discussed in the third part. The dilemmas of personnel are presented in the fourth part. The dilemmas are academic research of applied teaching, the centralisation and decentralisation of governance, economy versus quality, universality versus selectivity, the openness or closeness of profession, the flexibility or fixation of study process and others. The responsibility of university is discussed in the final part.