The purpose of this book is to study plurisubharmonic and analytic functions in n using capacity theory. The case n=l has been studied for a long time and is very well understood. The theory has been generalized to mn and the results are in many cases similar to the situation in . However, these results are not so well adapted to complex analysis in several variables - they are more related to harmonic than plurihar monic functions. Capacities can be thought of as a non-linear generali zation of measures; capacities are set functions and many of the capacities considered here can be obtained...