The whole is greater than its parts: life is not located in any of the parts of a living organism, but arises from the emergent properties of the whole they compose. Such emergent properties are the result of a ubiquitous trend towards self-organization.
Self-organizing principles are inherent in our universe and life is a direct consequence of self-organization. Therefore, both the origin of life and its subsequent evolution were inevitable. Kauffman refutes the theory that life started simple and became complex in favor of a scenario in which life started complex and whole due to a property of some complex chemical systems, the self-sustaining process of autocatalytic metabolism. Life is but a phase transition that occurs when the system becomes complex enough. Life is vastly more probably than traditionally assumed.
The theme of science is order. Order can come from equilibrium systems and from non-equilibrium systems that are sustained by a constant source of matter/energy or (udally) by a persistent dissipation of matter/energy. In the latter systems, order is generated by the flux of matter/energy. All living organisms (as well as systems such as the biosphere) are nonequilibrium ordered systems.
Kauffman advocates a "theory of emergence" that deals with nonequilibrium ordered systems. Such a theory would explain why life emerged at all.
Evolution is viewed as the traversing of a fitness landscape. Peaks represent optimal fitness. Populations wander driven by mutation, selection and drift across the landscape in their search for peaks. It turns out that the best strategy for reaching the peaks occurs at the phase transition between order and disorder (the "edge of chaos"). The same model applies to other biological phenomena and even nonbiological phenomena, and may therefore represent a universal law of nature.
Kauffman's view of life can be summarized as: autocatalytic networks arise spontaneously; natural selection brings them to the edge of chaos; a genetic regulatory mechanism accounts for ontogeny. Natural selection is not the only source of order: there is also order for free.
The main theme of Kauffman's research is that the requirements for order to emerge are far easier than traditionally assumed ("order for free").