The conceptual issues are made dominant in this second edition. This required to address in more detail those misconceptions which are the consequence of the profound difficulties of the subject and which travel from one publication to another. A new chapter titled Analogies, misconceptions and ill defined concepts was added along with a number of new sections on such topics as ergodicity, Eulerian versus Lagrangian descriptions, on validation of theories, on anomalous scaling and ill posedness of the concept of inertial range, on the Tennekes and Lumlety balance, and mathematics versus turbulence among others. Many of these are to a large extent a consequence of the series of lectures delivered in the Imperial College London in 2007 and 2008 in the frame of Marie Curie Chair in Fundamental and Conceptual Aspects of Turbulent Flows which was held by the author during the period June 1, 2006 – May 31, 2009.