This general book starts by surveying theories and experiments concerned with the origin of life; it then gives a sketch of new ideas and experiments by which the gaps in our understanding may be filled. The principal new idea is that a search for chemical models of primitive life which are highly tolerant of errors may result in the recognition of structures which do not involve exact replication of molecules. It is suggested that genes originated later, as parasites infecting an earlier non-replicating fauna. As the word origins in the title implies, the author suggests that we should look carefully at the notion that life began twice, once with cells and later with genes. The book is based on the Tarner lectures, given with the support of Trinity College, Cambridge, to a mixed university audience of educated but not expert listeners. It is therefore written for such a non-specialist reader.