While I am but a beginner when it comes to mathematical matters (freshman student at conjoined maths + physics programme) I must say that this book captivated me for last few hours. It strikes near-perfect balance between proofs, showcasing applications and theoretical musings while providing extensive explanations and explicitly calculated examples. If there was a solution manual for it I would, honest to anything you find holy, starve myself for a month to afford it :P.
I can recommend working through it as a companion to M. Spivak's Calculus on Manifolds. It's a great book and all, but it lacks a lot of commentary and requires solving pretty much all exercises to progress, making it less useful for people not yet accustomed to that type of learning (i.e. most people at first year maths/science courses).
Here is the authors course page.