The book consists of a presentation from scratch of cycle space methodology in complex
geometry. Applications in various contexts are given. A significant portion of the book is
devoted to material which is important in the general area of complex analysis. In this regard
a geometric approach is used to obtain fundamental results such as the local parameterization
theorem Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle spaces
have been used in complex geometry for some forty years. The purpose of the book is to
systematically explain these methods in a way which is accessible to graduate students in
mathematics as well as to research mathematicians. After the background material which is
presented in the initial chapters families of cycles are treated in the last most important
part of the book. Their topological aspects are developed in a systematic way and some basic
important applications of analytic families of cycles are given. The construction of the cycle
space as a complex space along with numerous important applications is given in the second
volume. The present book is a translation of the French version that was published in 2014 by
the French Mathematical Society.
