This book is a self-contained exposition on the Bohr-Jessen limit theorem. This limit theorem, which is concerned with the behavior of the Riemann zeta function $\zeta(s)$ on the line Re $s = \sigma$, where $1/2 \lt \sigma \leq 1$, was found by Bohr-Jessen in the early 1930s. After Bohr-Jessen, alternative proofs were given by Jessen-Wintner, Borchsenius-Jessen, Laurinčkas, Matsumoto and others. They dealt with this within the framework of probability theory. Their formulation, originated by Jessen-Wintner, is standard nowadays. The present book proposes a new approach for the formulation to refine their works. By this method, the whole story of the proof of the Bohr-Jessen limit theorem will now become clearer, so that the reader must be able to understand the essence of the proof in depth but without difficulty.