The aim of the opening speech is to present the most discussed issues in relation to inequality in personal distribution of income and wealth. In particular, it first examines the current trends in economic inequality (§ 1-4). Overall, some certainty has been achieved on these trends over the last century. In a second part of this opening speech (§ 5-7), some knowledge we have about pre-modern inequalities is summarized. In this regard, uncertainties are much more numerous than certainties.