TITLE: University-level books focusing on intuition?
QUESTION [16 upvotes]: I help some students with difficulties in Mathematics and Physics (especially math, physics, and engineering majors).
While in high school they usually don't study, or are not interested, etc., in university they seem to lack intuition, or simply they are taught to smother their own intuition with formalities they don't really understand.
I can occasionally come up with intuitive ideas, examples, pictures. Sometimes they come up with their own ideas, and ask me to check "if they got right what is behind". But this does not happen often, because they (and me) don't have much time to waste (or invest) in such "games". 
A full book which focuses on the intuitive aspects, in addition to their own official text, sometimes is exactly what we need. I am particularly fond of the book "Visual Complex Analysis" by T. Needham, for example. 
Are there any other books you know which focus on intuition, visualization, and understanding, rather than rigor and formalism?
Topics that would "call" for such a treatment are, in me and my students' opinion:

Differential forms and de Rham cohomology
Linear Algebra
Differential Geometry of Curves and Surfaces
Riemannian Geometry
Lie groups and Lie algebras (maybe with a focus on their applications to Mechanics, for physicists and engineers)
Relativity (special and general)
Probability and random processes.

Other topics are very welcome, too! (Also more advanced, if they exist.) 
We could rephrase the question as: What are the introductory books you wish you had known before?
Thanks.

REPLY [2 votes]: I'm too an student that you have mentioned who lacked intuition for mathematics in school and came aware after I reached college that the maths I learned was maths to pass an exam but not more than that.So I'm ready to help you as I can.
I'm also in a run to get into the intuitive world of Mathematics but don't know when will I complete the race.
Here are the books and links that I would suggest to get an intuition about Mathematics:

Christopher Cooper's Mathematics Notes by Christopher Cooper
Notes from Trigonometry by Steven Butler
Calculus made easy by Silvanus P. Thomspon
Statistics Online Learning by Penn State
Linear Algebra by Joshua
Cool Math(where you might get intuition about algebra and lines-within the section of algebra,which gives you line + algebra = linear algebra)
Last but not the least Math is Fun maintained by Rod Pierce(don't know much more) where you get intuition about basic mathematics.

Not to mention you could mail me if you want the offline versions of (4) and (7).Also don't worry about Copyright issues because all are free.