1. Background and some concepts. 1.1. Elastic and plastic regimes. 1.2. Griffith criterion: role of surfaces. 1.3. Peierls stress and barrier. 1.4. Dislocation core and atomic force. 1.5. Stacking faults. 1.6. Glissile and sessile dislocations. 1.7. Concept of fractals. 1.8. 'Glue' and related models of interatomic force fields. 1.9. Pair potentials. 1.10. Grain and twin boundaries. 1.11. Alloy formation: rules and models. 1.12. Friction mechanisms -- 2. Phenomenology and experiments. 2.1. Plastic deformation of bcc metals. 2.2. Phonons, electrons and plasticity. 2.3. High temperature strength of alloys. 2.4. The crack and fracture. 2.5. Power law relation between the plastic strain and the number of cycles to fatigue failure. 2.6. Statistical behaviour for the fracture of disordered media. 2.7. The roughness of the crack surface. 2.8. Dynamic instabilities of fracture -- 3. Introduction to extended defects and mechanical strength. 3.1. Some basic theory of crystal dislocations. 3.2. Elastic field of straight dislocation. 3.3. Interactions of dislocation with other defects. 3.4. Crystal lattice effects. 3.5. Dislocation motion over Peierls barrier. 3.6. Dislocations and cracks. 3.7. Geometrical aspects of grain boundaries. 3.8. Creep: example of single crystal of lead. 3.9. Superplastic materials. 3.10. Mechanical properties of fatigued fee crystals and their dislocation arrangements -- 4. Some characteristic features of fractals. 4.1. Self-similarity and fractals. 4.2. Self-similarity and dimension. 4.3. Hausdorff-Besicovitch dimension. 4.4. The Koch curves. 4.5. The cantor set. 4.6. The residual set and "fat fractals". 4.7. Statistical self-similarity. 4.8. Brownian motion and time series. 4.9. Self-similarity and self-affinity. 4.10. The relation of D to H. 4.11. Multifractal measures. 4.12. Percolation models of breakdown. 4.13. Fractal description of fractures. 4.14. Multirange fractals in materials. 4.15. Time evolution of multirange fractals. 4.16. Fragmentation. 4.17. Phenomenological relation between fractal dimension of fractured surfaces and fracture toughness of materials. 4.18. Physical sources of fractal surfaces -- 5. Elastic moduli and more general phonon properties. 5.1. Outline. 5.2. Force between half-planes of a metal. 5.3. Empirical relations between elastic moduli, vacancy formation energy and melting temperature.

6. Elements of electronic structure theory. 6.1. Free electron theory. 6.2. Exchange and correlation interactions. 6.3. Bulk modulus including exchange and correlation. 6.4. Structural stability of non-transition metals. 6.5. Elastic constants of hexagonal transition metals from electronic structure calculations. 6.6. Energy of simple metals as volume term plus pair potential contribution. 6.7. Pair potentials. 6.8. Structural stability of transition metals. 6.9. Electron density in interstitial region in metals. 6.10. Trends in vacancy formation energy with d-shell filling in transition metals. 6.11. Bloch's theorem and energy bands. 6.12. Pseudopotentials. 6.13. Coordination dependent and chemical models -- 7. Theory of pair potentials in simple s-p metals. 7.1. Thomas-Fermi theory of interaction between test charges in initially uniform electron gas. 7.2. Density functional theory of pair potentials -- 8. Transcending pair potentials: glue models of interatomic forces. 8.1. Introduction. 8.2. Embedded atom and related approaches 8.3. Embedded atom method: analytic model for fee metals. 8.4. Inequality relating vacancy formation energy in a hot crystal (near melting to rigidity). 8.5. Screw dislocation core structures for niobium and molybdenum. 8.6. Quantum-chemical model of cold metallic lattice energies as function of coordination number c. 8.7. Further work on dislocations and grain boundaries. 8.8. Friction, mechanical properties and interatomic interactions. 8.9. Empirical potentials vs density functional calculations for mechanical properties -- 9. Positron annihilation: experiment and theory. 9.1. Background. 9.2. Interaction of positrons with vacancies in metals. 9.3. Trapping model. 9.4. Positron-annihilation characteristics. 9.5. Electron and positron momentum distributions in solids. 9.6. Experimentation with low-energy positron beams. 9.7. Summary -- 10. Stretched chemical bonds, electron correlation and extended defect propagation. 10.1. Roughness and toughness of metals and metallic alloys. 10.2. Perfect crystal properties: elastic constants and melting points. 10.3. Morse potentials and crss of iron single crystals. 10.4. Plastic deformation of LI2 ordered alloys. 10.5. Breaking-bond models of propagation of extended defects. 10.6. Grain boundaries (GB), plastic behaviour and fracture.

The book is intended to describe the basic and newly developed elements of the physics of solids and materials science on mechanical properties of metals with as much continuity as is possible. Particular emphasis has been placed in atomistic and fractal approaches and continuum theory of dislocations is also introduced. Since the book is meant for the two main topics of progress in recent years, some interesting and important topics which have not been discussed or introduced are given in detail.For a long time, pair potentials were used very expensively in simulation studies. They can reproduce usefully total energies for many systems. But when one turns to elastic properties, fracture of surfaces, and the vacancy formation energy, deficiencies and limitations begin to emerge. These limitations of the simple pair potential approximation have been addressed by the development of empirical many-body potentials which is the major theme of our book.Over a decade or more, diverse scientists have recognized that many of the structures common in their experiments have a special kind of geometrical complexity. The key to this progress is the recognition that many random structures obey a symmetry that objects look the same on many different scales of observation. The concept of fractals was introduced by Mandelbrot and applied to fractures by himself and collaborators. Their work pointed to a correlation between toughness and the fractal dimension. Our interest is the fractal aspects of fractured surfaces. We will discuss more in our book.The strain field of a dislocation has a long range part and this part can be discussed rigorously from elasticity theory. Recent progress in elastic strain fields and dislocation mobility were made by Indenbom and Lothe. The elementary essentials will be introduced in our book