This is the 4th edition of a book originally published by Kluwer Academic Publishers. It is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects, with many advanced developments using mathematical spectral methods (two-point closures like the EDQNM theory), direct-numerical simulations, and large-eddy simulations. The book is still of great actuality on a topic of great importance for engineering and environmental applications, and presents a very detailed presentation of the field. The fourth edition incorporates new results coming from research work done since 1997. Many of these results come from direct and large-eddy simulations methods, which have provided significant advances in problems such as turbulent mixing or thermal exchanges (with and without gravity effects).