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emplifying their relevance to the problems at hand. My broader context is constituted by the ,,philosophy of chance" not only (or perhaps, not principally) in the theory of biological evolution, but also in the structure and evolution of the entire Universe, and my broader perspective is the historical perspective. Even though I do not intend to write a history of the concept of chance (if I did, it would have to be a work of considerably greater length), I wish, however, to focus on at least some episodes in the history of science and philosophy, namely those that have played a more important role in the formation of the concept and its transformations. History explains a number of problems, including those with which we struggle even today, often only because it never occurred to us that we should have examined their development through the ages. Looking at the evolution of the concepts connected with probability and chance, at the very outset we can see why we tend to associate the concept of chance (at this stage understood only intuitively) with the collapse of rationality. This association has made the process of domesticating random events considerably more difficult. After all, how one can understand something that is not rational? Help - yet over a long timeframe - arrived from two sources: from theological considerations - because chance may not break free from the embrace of Providence, and from the practice of gambling - because if one wants to win, one must somehow learn to control the randomness of chance. Thanks to the human passion for gambling, the exchange of letters between Pascal and Fermat constituted the foundations for what became later known as probability calculus, but soon this current was joined by theological strands at a key juncture: the notion of probability itself drifted in from theological disputes of Spanish casuists to the nascent probability calculus. The pace of events has since accelerated. Although in his seminal work Jacob Bernoulli still writes a lot about games of chance and hazard, they are more and more clearly replaced by purely mathematical theorems. Moreover, the practical applications of probability calculus testify to its maturity. For instance, mortality statistics have allowed the problem of epidemics in large cities to be overcome (since it was mostly there that reasonably accurate registers of the dead were maintained), and the application of statistical methods to the system of annuities began to bring profits to bankers. Thus ended the first stage of domesticating chance and thus ends the first part of this book. Then there is a gap. If I wanted to write a history of probability calculus, I would have to add here several chapters detailing what happened between Laplace (inclusive) and the beginning of the 20th century. No doubt, this would be interesting and might even shed quite a lot of light on a number of detailed issues, but would distance me from the main objective of this book - the philosophy of chance. For this very reason, I decided to jump straight to the 20th century. The beginning of the previous century saw the emergence in mathematics of processes with a fundamental impact on the understanding of chance and related concepts. Probability calculus quickly transformed from a collection of statements and rules useful in various applications into a theory of modern mathematics. Thanks to Andrey Kolmogorov, who noticed the relationship between probability and the mathematical measure theory, and his formalisation of probability calculus, the concept of probability was at last liberated from intuitive associations and became an effective tool for conducting formal analyses. Thanks to this development, probability theory as a special case of measure theory, entered into fruitful interactions with other mathematical theories, rising to the role of one of the key branches of contemporary mathematics. Interpretative problems, so important for the philosophy of chance did not disappear, but even here formalisation proved to be helpful in that it made it easier to perceive the boundary between the purely formal structure and its interpretative circumstances. Progress in mathematics usually leads to generalisations. The fact that probability appeared in quantum mechanics in a new role, so to speak, not only intensified interpretative disputes, but also became a harbinger (or even a preliminary stage) of a generalisation of this concept. The process, once initiated, continued apace. Today, we have at our disposal a number of generalisations of probability theory (or, more accurately, probabilistic measure) of which the most spectacular include the so-called noncommutative probabilistic measures. Their particular beauty consists in that generalised concepts of probability possess a host of properties which are completely surprising from the vantage point of our mental habits. The concept of chance is evidently connected with the notion of probabili