Undergraduate maths textbooks for self-learners

Question

I am a junior student majored in mechanical engineering. I have great passion for pure and applied math.Sadly, the maths disciplines in my university did not fulfill my requirements.For now, I have self learned Analysis with a single variable(chapter 1-7 of baby rudin) and Axler's entire Linear Algebra Done Right. I want to keep studying on the following topics:Multivariable Analysis / Modern Algebra (groups,rings,which didn’t covered in Axler’s textbook) Any good textbooks or website recommendations for me? The book should be rigorous and well explained. More importantly, it should be friendly to self-learners. It may also has the solution manual or at least some hints for the problem. Because it is hard for a non-math majored students to get professional assistance.

Answer 1

For groups, rings and other topics from modern algebra, I highly recommend Dummit and Foote's Abstract Algebra. It is comprehensive and very student friendly.

For multivariable calculus, there are several good recommendations you can find here: References for multivariable calculus

Answer 2

I found the following Youtube videos by Dr.Matt Salomone really useful as well on Abstract Algebra.

https://youtu.be/N-5Av1KC11w