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This introductory chapter discusses such notions as determinism, chaos and randomness, p- dictibility and unpredictibility, some initial approaches to formalizing r- domness and it surveys certain problems that can be solved by probability theory. This will perhaps give one an idea to what extent the theory can - swer questions arising in speci?c random occurrences and the character of the answers provided by the theory. 1. 1 The Nature of Randomness The phrase “by chance” has no single meaning in ordinary language. For instance, it may mean unpremeditated, nonobligatory, unexpected, and so on. Its opposite sense is simpler: “not by chance” signi?es obliged to or bound to (happen). In philosophy, necessity counteracts randomness. Necessity signi?es conforming to law – it can be expressed by an exact law. The basic laws of mechanics, physics and astronomy can be formulated in terms of precise quantitativerelationswhichmustholdwithironcladnecessity.