Advances in technology are demanding ever-increasing mastery over the materials being used: the challenge is to gain a better understanding of their behaviour, and more particularly of the relations between their microstructure and their macroscopic properties. This two-volume work, of which this is the first volume, aims to provide the means by which this challenge may be met. Starting from the mechanics of deformation, it develops the laws governing macroscopic behaviour - expressed as the constitutive equations - always taking account of the physical phenomena which underlie rheological behaviour. The most recent developments are presented, in particular those concerning heterogeneous materials such as metallic alloys, polymers and composites. Each chapter is devoted to one of the major classes of material behaviour. As the subtitles indicate, Volume I deals with elasticity and plasticity and Volume II with viscoelasticity, viscoplasticity, damage phenomena, and the mechanics of fracture and of contact. Annexes to Volume I give the relevant basic tools and techniques of continuous-media mechanics, crystallography and phase changes. Most of the chapters end with a set of exercises, to many of which either the full solution or hints on how to obtain this are given; each volume is profusely illustrated with explanatory diagrams and with electron-microscope photographs. Mechanics of Material Behaviour grew out of the Paris Diplome d'Études Approfondies (DEA, Advanced Studies Diploma) in Mechanics and Materials. In addition to Diploma-level students, it is addressed to students reading for a first degree in engineering, practising engineers and research workers in this field. The treatment is mathematical but the mathematical arguments should not prove difficult; the real difficulties of the subject stem from the frequent and considerable changes of scale that have to be appreciated and the need to acquire a firm grasp of the underlying physics.