This volume consists of ten expository articles describing processes of evolution via natural selection in stochastic environments. Maintaining an elementary level throughout, the authors describe the latest researches in the mathematical theory of adaptation in stochastic environments. Topics discussed include: history of past research; fitness optimization criteria; environmental and demographic variability; life-history evolution; evolutionarily stable strategies; population dynamics of age-structured populations; phenotypic plasticity and imperfect information; evolution of behavioural adaptations; methods of quanitifying environmental predictability; genetics of conditional strategies; the co-existence of multiple life-history strategies; and adaptive learning.