This book is a selection of Masatake Kuranishi's papers. Born in 1924, Kuranishi produced deep and far-reaching results in geometry over his career. Of his voluminous contributions, this book focuses on his later works: (i) his work on locally complete families of deformation of compact complex manifolds. Kuranishi was first to prove the fundamental results of the existence of complete families whose parameter spaces are today called Kuranishi spaces. His result is highly influential in deformation theory of various geometric objects. (ii) His work on the local embedding problem of Cauchy–Riemann structures. Kuranishi proved a fundamental embedding theorem in Cauchy–Riemann geometry. (iii) His work on Cartan Geometry and Szegö kernels. Mainly for his works on (i) and (ii), Kuranishi was awarded the Bergman Prize in 2000. Today, he is a professor emeritus of Columbia University.
