The classical subjects are treated in a classical way. Here is a list: rounding errors, approximation and interpolation, differentiation and integration, zero finding for (systems of) nonlinear equations, ODE's: initial, as well as boundary value problems. Note however that numerical linear algebra, optimisation and PDE's are absent.
The author concentrates on the analysis and basic principals of the methods and the algorithms. The text is never very abstract, i.e., there are some theorems and proofs, but they certainly do not dominate. For the more difficult parts, the reader is referred to the literature and/or some comments are given at the end of a chapter. This makes the theory easily digestible and never dull.
There is a lot of matab code included to play with and so one can gain some feeling of what the theory means in `practice'. However, there are no real life examples from applied fields like engineering, economics, etc. Even the academic ones are rare.
On the other hand, there is an amazingly extensive list of `theoretical' exercises (i.e., proving or deriving things with paper and pencil) but also some machine-assignments per chapter.
The second edition has updated references and notes, and matlab has now been adapted as the sole computer language. Some exercises are added and the book's subtitle `an introduction' in the previous edition has been dropped. The major change is however that now solutions to all exercises and computer assignments are available. A selected number is included after each chapter, but all of them are available as a pdf to instructors upon request from the publisher on the book's webpage. It's a pity that it is not possible to download the matlab code as well. On that webpage one can also find a list of typo's that should be corrected.
Conclusion: one of the better handbooks on the market today, based on several decades of teaching experience of the author. It is an excellent tool for teaching a classical numerical analysis course.