An alternative programme, to be approached mostly in this order:
1: LINEAR EQUATIONS
P M Cohn. Routledge & Kegan Paul, 1958
2: SETS AND GROUPS
J A Green. Routledge & Kegan Paul, 1965
3: A FIRST COURSE IN MATHEMATICAL ANALYSIS
J C Burkill. Cambridge U P, 1962.
4: LECTURES ON ORDINARY DIFFERENTIAL EQUATIONS
Wiltold Hurewicz. MIT Press, 1958; Dover, 1990 and 2014
5: INTRODUCTION TO COMPLEX ANALYSIS
H A Priestley. Oxford, 1985 and 1990
6: TOPOLOGY FROM THE DIFFERENTIABLE VIEWPOINT
John W Milnor. Princeton, 1965 and 1997
0: COUNTEREXAMPLES IN ANALYSIS
Bernard Gelbaum and John Olmsted
Holden-Day, 1964 and Dover, 2003
9: THE PRINCETON COMPANION TO MATHEMATICS
T Gowers, editor. Princeton, 2008
A reader is encouraged to skip subtleties and get an impression of the overall structure of the subject. Better not try to master every detail until it is really needed or you realise it is fascinating.