These notes represent the outgrowth of an offer bу Princeton University to let me teach a graduate level course in cobordism theory. Despite the fact that cobordism notions appear in the earliest literature of algebraic topology, it has only been since the vork of Thom in 1954 that more than isolated results have been available. Since that time the growth of this area has been phenomonal, but has largely taken the form of individual research papers. To It oertain extent, the nature of cobordism as a classificational tool has led to the study of many individual applications rather than the development of a Qintral theory. In particular, there is no complete exposition of the fundamental results of cobordism theory, and it is hoped that these notes may help to fill this gap.