Eli Bendersky's website The main topic tackled in this book is the level at which natural selection acts. Ask a random person (who groks natural selection and Darwinism) and you will most probably get an answer that natural selection acts at the level of the organism. Some will even go farther to say that sometimes natural selection acts at the level of groups of organisms, even species.
Dawkins, however, thinks differently. Though I'm pretty sure that he claimed it in The Selfish Gene as well, this book is entirly dedicated to demonstrate that natural selection acts at the level of the gene.
In his own words (p. 4):
The thesis that I shall support is this. It is legitimate to speak of adaptations as being 'for the benefit of' something, but that something is best not seen as the individual organism. It is a smaller unit which I call the active, germ-line replicator. The most important kind of replicator is the 'gene' or small genetic fragment.
Seeing how organisms compete is easy and intuitive, but what does it mean for genes to compete ? Dawkins makes a crisp definition (p. 154):
Natural selection at the gene level is concerned with competition among alleles for a particular chromosomal slot in a shared gene-pool.
Moreover, since the basic unit of natural selection is the gene, its effects are not even confined to individual organisms. The organisms are a convenient but arbitrary frontiers for the phenotypic effects (external expressions) of genes, hence the 'extended phenotype' (p. 248-249):
[...] I have amended this to a new central theorem of the extended phenotype: An animal's behaviour tends to maximize the survival of genes 'for' that behaviour, whether or not those genese happen to be in the body of the particular animal performing the behaviour. [...] I am suggesting that the individual performing the behaviour is not the entity for whose benefit the behaviour is an adaptation. Adaptations benefit the genetic replicators responsible for them, and only incidentally the individual organisms involved.
While this book expounds important points, I have a word of warning. It is not intended for the lay reader, but rather for a professional student or practitioner of genetics and biology. As Daniel Dennett says in the afterword (p. 266):
The Selfish Gene was written for educated lay readers, and glided over many of the intricacies and technicalities that a proper scientific assessment needs to consider at length. The Extended Phenotype was written for the professional biologist, but so graceful and lucid is Dawkins's writing that even outsiders who are prepared to exercise their brains vigorously can follow the arguments, and appreciate the subtlety of the issues.
Now, if Dennett, one of the most brilliant philosophers of the 20th century, notes that one has to exercise his brain vigorously to really understand the book, take it as a dire warning. This book is no pop-science. I, for once, having read a few of Dawkins' books and many others on evolution and Darwinism, found it very hard to follow, and almost impossible to read more than a few pages in a single sitting.
In some places Dawkins writes as if the book is just another scientific article (which, in a sense, it is). Pages upon pages of references to other books and papers, arguments from one author to another, and so on. Not very easy to follow, indeed.
So would I recommend this book ? I'm not sure. If you haven't read at least 5 other books on natural selection, Darwinism and genetics, definitely stay away. If you're more knowledgeable in these topics, you might find this book an interesting, though very challenging read. For people with professional interest in genetics, the book is probably a must, because it sets this exciting field in the (almost certainly) correct philosophic framework.