Humans have come to dominate the world through innovation. People can build upon knowledge and others' work to create new things. Even something simple like a pencil is behind the scope of any single person to easily create on their own. They would need to cut down trees, mine metal, and do all the work to shape and form it. It would be a daunting task. Today it is easy to buy a pencil at the local store. Many people have been involved in the process to make the pencil, yet they don't have the knowledge and skills outside their realm.
The author has great faith in the ability of humans to innovate their way out of problems. However, he has little faith in us being able to predict what innovations will take place. He sees government intervention as often a fools errand. Subsidizing big companies that were previous innovators merely delays their eventual fall. The smaller, newer, more nimble organizations are the ones that provide most of the advantage to society. These small companies then become big ones and often ossify. Governments tend to favor them because they are big, yet that is a mistake. Governments also attempt to regulate activities based on what is currently known. This can interfere with truly useful innovations. Many of the problems in poor countries can be traced to rent-seeking leaders. The institutions are corrupt making it difficult for anything to get done. Even with foreign aid, the poor often remain poor, while the leaders are getting rich.
The author has little respect for pessimist alarmists. Negative fear-mongering does get a lot of coverage. He catalogs big fears such as "overpopulation", "acid rain" and "global cooling" that have all fallen by the wayside. Today, "global warming" is the boogeyman. He acknowledges that the earth is warming, but objects to many of the actions that are taken. Climate change will cause changes. However, humans have always dealt with climatic changes, and could continue to deal with it. Even in some of the worse case scenarios, the total risk is not worth significant societal changes.
The "fixes" can be worse than the problem. Some of the "renewable" resources such as biofuels require great amounts of land and can be a net negative for climate change. Even "green energy" like wind is very inefficient. Legislation often greatly subsidizes forms of "green" energy production we know about, which my stall some of the needed innovation. Fossil fuels are amazingly efficient and have replaced previous forms of energy (such as slaves and animals). They have also long outlasted their predicted depletion thanks to increases in extraction and usage efficiency. We likely have a solution to our energy problems waiting to be created. The solution probably is not something that we think of (electric or self-driving cars), but instead something totally new.
Is there a limit to how we can innovate out of our problems? Yes. This has been seen in previous cultures. In the middle ages, both China and the Muslim chose stability over innovation. Government policies have often forced innovation down the wrong track. Perhaps we will run into something that we just can't make better. However, if we do, government will not be able to help us.
Matt Ridley is very strongly pro-science, yet is not afraid to ruffle feathers or bump against orthodox views. Although Genome is over two decades old, he picked a writing approach that makes it still worthwhile. He takes us on a "tour" of the human genome, going chromosome by chromosome.. For each one, he picks something that is relevant. It may be a disease that is associated with it. It may be a well known gene associated with a specific location such as Huntington's disease. Or it may be looking at a location where researchers thought they found something interesting. The history is still interesting even as many things have changed since the book was written.
Atheist Evolutionary Predestined Libertarianism. That pretty much sums up the Ridley's principles. He is advocating the opposite of the "great man" view of history. Everything was destined to happen. Some people may slow progress through their interventions, but can do little to help things along. The best course of action is for government and culture to get out of the way and let things happen. 
Innovation happens best when people have the means and the hunger. Government often steps in to remedy the excesses. Alas, these remedies often make it easier for the entrenched behemoths to manage, while making it more difficult for the nimble entrepreneurs to grown. When societies focus more on collective comforts and equity, innovation will often stall. While we like to admire the insightful inventor, inventions are often "destined to happen". It is very common for several people to have the same innovation at the same time. This is often due to the environment that existed at the time. Innovations are usually based on incremental changes rather than drastic switches in direction.
The Red Queen hypothesis comes from the character in Lewis Carrol's Through the Looking Glass who is always running in order to keep in the same place. Sexual selection must be used as part of the mechanism to continually evolve and adapt in order to stave off extinction. The book starts by asking "why sex?" It seems a very inefficient way to pass on genes. After all, why not just clone oneself to pass on all genes? There are many theories. The "change" is a key benefit. There are chances to clean up "mistakes" or introduce "new mistakes". It also encourages social behaviors. Different animals have adapted in various ways due to their mating patterns. Sex selection also happens in various manners (sometimes based on things such as temperature.) Humans are rather unique in not knowing the precise time of fertility and not producing off-spring that are "done" yet. (The "big brains" need to fit through the small birth canal.) People seem to have an in-built incest restriction against mating with people we have grown up with. Other mating rules have differed across cultures. Monogamy has become a common way to ensure the child has two parents to help with raising. Polygamy may benefit a few men at the top of the hierarchy, but in general it benefits women who now have greater access to the alphas. Men seek traits in women that allow for the production of more offspring (such as youth.)