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 the utmost 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). Topics dealt with include: an introduction to turbulence in fluid mechanics; basic fluid dynamics; transition to turbulence; shear-flow turbulence; Fourier analysis for homogeneous turbulence; isotropic turbulence; phenomenology and simulations; analytical theories and stochastic models; two-dimensional turbulence; geostrophic turbulence; absolute-equilibrium ensembles; the statistical predictability theory; large-eddy simulations; and a section that explores developments towards real-world turbulence.