This book is destined for scientific workers and professors in the field of quantum mechanics and quantum theory of collisions, students and post-graduate students and all interested in quantum mechanics, quantum field theory and nuclear physics. The book contains the chapter of fundamental quantum mechanics and quantum field theory – on time as a quantum observable for systems with continuous and discrete spectra. In its completed form this book could not be written up to now due to a number of the mathematical problems. Some mathematicians had been known the solution of these problems in the field of operator theory in Hilbert spaces for systems with continuous energy spectrum. But practically these problems were unknown for almost of all physicists, with the exception of the author and his friend. Overcoming these and other mathematical problems permitted finally to develop and apply the methods of time analysis of quantum processes and write this book. Moreover, in it there are exposed also many applications of time analysis of quantum processes and paradoxes for tunneling and collisions (nuclear reactions)which were elaborated by author, partly together with colleagues.