Notes based on a series of lectures delivered at the University of Montreal's Center for Mathematical Research in 1990 serve as a rapid introduction to topics in transcendental algebraic geometry centered around the general Hodge conjecture, for non-specialists and advanced graduate students. Topics include complex manifolds, vector bundles, Chern class theory, and Chow groups. Assumes some familiarity with differential geometric concepts such as Stoke's theorem and de Rham cohomology, and a course in algebraic geometry. This second edition incorporates recent developments in the field. Annotation c. Book News, Inc., Portland, OR (booknews.com)