It is a pleasure to write a preface for the second edition of Mathematical Analysis: A Straightforward Approach. The first edition was well-received and I have therefore thought it wise to leave its text substantially unaltered except for one or two minor points of clarification and the correction of misprints. The major change is the addition of two long chapters on analysis in vector spaces for which there has been a considerable demand. These get as far as the idea of a derivative as a matrix and the use of the second order derivative of a real-valued function in classifying stationary points. More advanced material than this would seem to me better delayed until after the basic topological notions have been mastered. As far as the material covered is concerned, it does not involve the proof of many theorems and the necessary proofs involve no new analytic ideas. However, the material does require a certain facility with algebraic and geometric ideas and students with only a very limited knowledge of linear algebra may find it heavy going in spite of the fact that some discussion of the necessary concepts from linear algebra is included where appropriate. Another innovation is the inclusion of a collection of further problems for which the solutions are not given. I am grateful to John Erdos for some of these as well as other helpful suggestions.