This text was produced for the second part of a two-part sequence on advanced cal
culus, whose aim is to provide a frm logical foundation for analysis, for students who
have had three semesters of calculus and a course in linear algebra. The frst part trea ts
analysis in one variable, and the text  was written to cover that material. The text at
hand treats analysis in several variables. These two texts can be used as companions,
but they are written so that they can be used independently, if desired.