I'm using gap year to prepare for B.S. in electrical engineering. Currently I'm solving through Spivak's "Calculus", Lang's "Introduction to Linear Algebra" and Velleman's "How To Prove It." I have three books on analysis, Rudin's "Principles of Mathematical Analysis", Abbott's "Understanding Analysis" and Needham's "Visual Complex Analysis." Now, as I understand real analysis should come before complex. So the question is between Abbott and Rudin. Namely, is analysis background from Spivak good enough to jump into Rudin and skip Abbott? I know Spivak isn't a real analysis book, but more like a bridge between analysis and calculus. I've also heard that Rudin can be a headache to read so I'm wondering if I should tackle it or go through Abbott first, which seems more "user friendly." Although Spivak is fixing the situation, my calculus isn't very consistent because until now I've been cherry picking topics that seemed more interesting and pouring time in learning those instead of climbing consistently. For example, I have no problem with things like Gaussian quadrature or Lagrange multipliers but I'm by no means solid on series.