Here is my list. I tried to make it more practical by supplying links to electronic versions whenever possible.
Rudin: Principles of mathematical analysis
Electronic version: http://gen.lib.rus.ec/get?nametype=orig&md5=0AB81110FEE9FBF5C218F772AB137601
Kostrikin, Manin: Linear Algebra and Geometry
[Sorry, couldn't find an electronic version of this book.]
Cartan: Elementary theory of analytic functions of one or several complex variables
[Sorry, couldn't find an electronic version of this book. However, Dover offers an inexpensive paperback edition for $9.]
Shafarevich: Basic notions of algebra
Electronic version: http://gen.lib.rus.ec/get?nametype=orig&md5=11154CB5CF3714C07D0D20FB3C79D803
Milnor: Topology from the differentiable viewpoint
Electronic version: http://gen.lib.rus.ec/get?nametype=orig&md5=E78E64CD53429CC8DD94D7282E2BDA27
Hatcher: Algebraic topology
Electronic version: http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Helemskii: Lectures and exercises on functional analysis
Electronic version: http://gen.lib.rus.ec/get?nametype=orig&md5=A18C3A9EC500745D563F9D3816892E3B
Milnor: Morse theory
Electronic version: http://gen.lib.rus.ec/get?nametype=orig&md5=ACD9C232FDFD205E937583F301F20058
Serre: A course in arithemtic
Electronic version: http://gen.lib.rus.ec/get?nametype=orig&md5=C00F38F10D80A59AF2A64B3D6D427CFC
Edit: I rearranged the list so that books appear more or less in order of increasing difficulty and prerequisites of every book precede it in the list.