*(English)*Zbl 0870.73004

In every rapidly developing scientific branch – and continuum physics is such one – it is once in a while desirable that someone undertakes the difficult task to review and summarize the state-of-the-art. That means to gather all the different theoretical suggestions, select from this vast manifold the convincing and promising ones, translate them into one language, express them in a precise notation, and finally assemble them in a compact and readable work. The last time this was done in the 60s in the context of the famous Handbuch der Physik. After more than three decades, there is again great need to update the matter.

Šilhavý’s work is a welcome contribution in this direction. At least it fulfills the important requirements for such a review. Firstly, it starts from the very fundamental concepts of continuum mechanics and thermodynamics. Secondly, it covers the broad range up to very recent advances in this field such as phase changes, a very trendy issue. Thirdly, the author uses precise mathematical language to clearly present these concepts. And, last, but not least, he gives a rather broad overview of different schools and theories in the field.

A general theory of continuous media has not yet been completed and finalized, and Šilhavý alone, of course, it not able to do it, although he could remove many deficiencies and bridge many gaps with his own ideas. Some of the concepts that are presented still appear unnatural, if not awkward. For example, the introduction of the state-space, being a fundamental concept for both mechanics and thermodynamics, does not have the desired clearness. But these deficiencies are inherent to the current state-of-the-art and not due to the author.

There is no doubt that the book is a rich source of insight and will be a great help to all researchers in the field. For some readers it might be too mathematical and too far from applications. For other it will surely not be mathematical enough. So, perhaps, the author has found the right compromise between two extremes. At least the referent considers it as a work of great interest and stimulus and warmly recommends it to other researchers.