Hi! I am looking for a very rigorous book on some of the topics covered in Calculus of Multiple Variables. My University uses the last part of Adams "Calculus: a complete course" and I found the presentation therein more fit for people needing to know enough to perform the calculations than for those who want to understand the concepts... At best it could also cover implicit functions and vector fields In addition to vector calculus ( multiple integrals and the other content I am currently satisfied with what I know so far, so it's no need for it to be included) So you'll know a bit more about my level: Books I've studied so far include baby Rudin, Carothers "Real Analysis", parts of the (first 7 chapters) "Big Rudin", the "complex variables"- book of Brown & Churchill. I also have studied much of the Fraleigh's "Introduction to Abstract Algebra", but that's a book I don't understand to well (especially after the first 10 chapters or so). However I want to go back to the Calculus III content and study it in a far more rigorous way than the treatment in Adams' book. I have read some of the other threads and I feel many are asking for a good book to introduce themselves to the subject. Thus I am not sure which book will be the best for my level, what would you recommend? Any suggestions would be greatly appreciated!