This book presents the Theory of Differential Calculus and Holomorphy
in its modern setting of infinite dimensional (locally convex) spaces.
Although this subject has very old roots stemming back to the last century,
it has grown very rapidly in the recent years, and most of the results in￾cluded in this book were available up to now only in article form and,
therefore, not really accessible to the non specialist. Furthermore one
may reasonnably believe that the general aspect of the Theory will certainly
not change fundamentally in the future. Several books on Differential
Calculus or on Holomorphy in locally convex spaces already exist, but they
do not contain most of the results presented here, which nevertheless have
a fundamental character in the Theory.