The Red Queen of the title refers to the character in Through the Looking-Glass who tells Alice she has to run as fast as she can in order to remain in the same place. As the subtitle indicates, this epitomises, for Ridley, the role of sex in evolution.
Unless one has thought about it, the need to explain the existence of sex is not obvious, so widespread is it in both plants and animals. Yet there is a puzzle, for calculation shows that if an organism reproduces asexually it should multiply faster than its competitors and hence out-compete and replace them. So sexual reproduction must have some advantage that isn't immediately obvious. Its main effect is to produce individual members of a species that have a wide range of genetic make-ups, but why is this variability beneficial? The most favoured theory at present is that it provides resistance to parasites. All organisms are in a constant arms race against parasites; each new defence mechanism that evolves is countered by a new attack weapon produced by the parasites. Hence the Red Queen: organisms have to keep evolving new defences to keep pace with the threat from parasites.
Another puzzle concerns the existence of "costly" sexual characteristics, such as the peacock's tail. Extraordinary advertisements like this make their possessor more vulnerable to predators, so why have they evolved? The answer was suggested by Charles Darwin, who postulated what he termed sexual selection. Females choose mates who have the most resplendent adornments and this favours the development of still more resplendent adornments. Certainly there is a cost associated with the possession of these extravagances but, like Victorian follies, they provide evidence for the prosperity (good health) of their possessor. Animals which carry a large weight of parasites are generally unable to produce fine secondary sexual characteristics.
The setting forth of this theory of sex occupies the first half of the book; the second half applies the theory to human beings, and this is naturally the part that is most likely to be contentious. Ridley discusses monogamy versus polygamy, sex differences in personality characteristics, and the nature of sexual preference. Ridley holds that these things have an evolutionary origin. Much of this is likely to excite violent disagreement from ardent feminists who hold that psychological differences between men and women are determined by society, not biology. I myself find his arguments (which are not, of course, by any means original) persuasive, but in any case they are readably and cogently expressed and the book provides a good introduction to the issues.