The book gives an accessible account of modern probabilistic methodsfor analyzing combinatorial structures and algorithms. It will be anuseful guide for graduate students and researchers. Special featuresincluded: a simple treatment of Talagrand's inequalities and theirapplications; an overview and many carefully worked out examples ofthe probabilistic analysis of combinatorial algorithms; a discussionof the "exact simulation" algorithm (in the context of Markov ChainMonte Carlo Methods); a general method for finding asymptoticallyoptimal or near optimal graph colouring, showing how theprobabilistic method may be fine-tuned to exploit the structure ofthe underlying graph; a succinct treatment of randomized algorithmsand derandomization techniques.