What is Life? is an absolute classic. Schrodinger felt that life must be explainable by physics and chemistry, yet seemed to violate the normal behavior of entropy-- and he understood further that this was a remarkable wedge point to explore. He figured out the explanation: life is the result of evolution of genetic information, which selects for complex processes that by ordinary considerations would be very unlikely. He predicted that there must be a molecule capable of carrying the genetic information (incorrectly thinking it would be a protein.) His beautifully-written book was influential and timely. Within 4 years, Von Neumann elucidated the mechanisms involved in self-reproducing automata (illustrating his abstract discussion with a picture looking remarkably like DNA to the eyes of readers today); and within a decade, Watson and Crick grasped the structure of DNA. You should not read Schrodinger's book today as one of your first sources to understand life-- there has been remarkable progress in the 50 years since Watson and Crick-- but you should read it to gain appreciation for how science can be advanced when the time is ready and a wedge point, an apparent conflict between fundamental ideas, is analyzed.
The volume also includes another lecture by Schrodinger, Mind and Matter, which is historically interesting in another way. In Schrodinger's day, the state of understanding had not advanced to the point where it was possible to make as useful conjectures about the structure of mind as of life, and he accordingly felt "[mind] may well be beyond human understanding."
Readers interested in Schrodinger's book will also enjoy What is Thought?, published 2004. What is Thought? argues that mind must be explainable by computer science, that the fundamental issues are computational, and that there is again a wedge point: the question of how the workings of a computer, which are always purely syntactical, can correspond to meaning and understanding. The situation is parallel to the one that faced Schrodinger with respect to life in two respects: first, mind is the outcome of evolution, which has built thought processes that seem inconsistent with our standard science, and second, scientific research has advanced to the point where, if we focus on the wedge point, significant understanding is obtainable. What is Thought? brings to bear on the problem of mind core ideas from computational learning theory, complexity theory, and evolutionary computing, as well as molecular and evolutionary biology, cognitive science, and other areas. The result is a principled and concrete explanation, consistent with the vast array of available data, of how meaning, understanding, language, consciousness, and all the various aspects of mind arise from execution of an evolved computer program.