The book begins with an exposition of the interesting history of magnetism and magnetic materials. This is followed by a short chapter discussing the role of magnetism and magnetic materials in modern society and current technological applications of magnetic materials and devices. This second chapter highlights why magnetism is considered to be more of an applied or experiemntal science rather than a theoretical one.

The meaning of the stress tensor is elucidated and its representation with the Mohr circle is presented.

Symmetry is introduced as a basic notion of physics and, in particular, for soil mechanics also. Isotropy and anisotropy are discussed. A special case of isotropy of space is the principle of material frame indifference which plays an eminent role in the development of constitutive equations. The geometric scaling is discussed together with the notion of a simple material, which is – often unconsciously – basic in geotechnical engineering. Invariance with respect to stress and time scales is discussed. Mechanical similarity and the associated Pi theorem is shown to be the basis for the evaluation of so-called physical simulations with model tests.

A very short and simple introduction to vectors and tensors and some related quantities.

It is shown that the typical paths obtained with element tests can be inferred by reasoning if some basic properties of proportional paths are taken into account.

The notion of collapse and its importance in geotechnical engineering is introduced. The two main approaches are explained: (i) stress fields that fulfil the Mohr–Coulomb limit condition (together with slip line analysis as an application of the method of characteristics) and (ii) analysis of collapse mechanisms consisting of rigid blocks. The harmonisation of codes and the problematic definition of safety on the basis of probability theory are discussed.

As an important application of the theory of elasticity in soil mechanics, the main principles of elastodynamics are introduced. On the basis of waves in 1D-continua the notions of transmission, reflexion and dynamic stiffness are explained, and the body waves are presented as compression and shear waves. Rayleigh waves are presented as an example of surface waves.

The general definition of elasticity is given, and as a special case the linear elasticity with Hooke’s law, is presented together with its derivation on the basis of the Cayley–Hamilton theorem. Some applications of elasticity theory in soil mechanics are presented.

Soil consisting of grains, water and air is an example of a multiphase material (or mixture). The basic concepts for multiphase materials, such as volume fraction, partial quantities and interaction forces are introduced. The Darcy's equation and balance equations for mixtures are introduced.

On their basis, the consolidation theory is presented. The equations describing steady and unsteady groundwater flow are derived. Transport within groundwater by means of convection, diffusion and dispersion is explained. The main principles describing unsaturated soil are presented: capillary and osmotic suction, the function of filters is explained. The soil–water characteristic curve is also introduced. The effective stresses in unsaturated soil are discussed.

The notion of constitutive equations (or laws) is elucidated together with the meaning of related notions such as material constants, calibration and response envelopes. Also discussed is why a comparison of constitutive equations is conceptually difficult.

Several tensors that describe deformation are introduced, as well as stretching and spin. As an example, they are presented for the special case of simple shear. The compatibility equations are discussed together with non-Boltzmann continua.

The mechanical behaviour of soil is introduced by presenting and discussing the typical outcomes of element tests with soil.