The book is an outcome of two conferences held in Poland in 1987 and 1990. Both conferences dealt with the problem of rationality; the first put the problem in the context of the philosophy of Popper and Polanyi; and the second involved the notion of the aim of science. This book presents the most comprehensive current account of the manifold approaches to the problem of rationality and related issues. Generally speaking, some authors are convinced that the standard approach to the problem of rationality is more or less correct. They try to amend this approach and/or to reply to some objections to it. Others adopt a more radical attitude and seek inspiration in more exotic regions of philosophy of science, in particular in the philosophy of Michael Polanyi. In this case not only the problem of rationality of science is addressed but also the problem of rationality of the philosophy of science itself. What makes the book really fascinating is the common attitude of all authors in addressing fundamental issues pertaining to the problem of rationality. This results from the fact that both conferences were organized for a small number of participants and there was time for discussion within a friendly but demanding social environment. The book is primarily intended for researchers in the philosophy of science. It is also valuable to other philosophers interested in current trends in philosophy of science, to scientists of various disciplines interested in philosophy, to scientists and to graduate students in the philosophy of science.