I would like to study university level mathematics on my own. I found rigorous books on single variable calculus and topology and learned those. But what would one recommend for several variable calculus? I found a lecture notes but there were many details omitted and for example Taylor polynomial was given only a special case and there was no material included to address how to estimate the error in Taylor's polynomial.
Previously I have read this book (the link is to a .pdf file) and some lecture notes by Olli Martio. I was unable to find those note from the Internet. Also I read the book Topologia by Jussi Väisälä. Those are Finnish books but English material would be fine.