<p>The present volume stems from a book-proposal made about two years ago to College&nbsp;Publications, London. The main idea was that of <em>illustrating the interplay between&nbsp;the contemporary work in logic and the mainstream mathematics.</em></p><p>The division of the volume in two sections &ndash; topics in &lsquo;logic&rsquo; vs topics in &lsquo;computing&rsquo;&nbsp;&ndash; is more or less conventional. Some contributions are focussed on historical&nbsp;and technical details meant to put in perspective the impact of the work of some&nbsp;outstanding mathematicians and philosophers on the contemporary research in logic&nbsp;and computing science. Some other papers, also with a historical flavour, were supposed&nbsp;to evidentiate punctual methods of research and specific concepts or topics,&nbsp;as, e.g., decidability, computability, randomness, and computational or descriptive&nbsp;complexity. In general, the papers were intended as <em>specific surveys of results.</em></p><p>Other volumes &ndash; to be issued subsequently in the same series &ndash; will hopefully&nbsp;delineate aspects of the <em>contemporary logic landscape</em> that have not been illustrated&nbsp;here.</p><p>The intended audience of the book includes graduate students in mathematical&nbsp;logic, foundations of matematics, and computing science, as well as philosophers,&nbsp;mathematicians, and, possibly, other scientists interested in the recent research on&nbsp;logic and computing.</p>