I remember having a hard time understanding limsup/liminf and only actually understood the concept after reading this book. I am sure it is not for everyone due to its age, but I think this book is a much better introduction than baby Rudin.
Personally I would read a book on statistical physics instead, since this is where the study of 'emergence' began. The Feynman lectures would be good for this.
Great. The OUP book linked above viz. Introduction to the Theory of Complex Systems by Stefan Thurner et al. looks particularly good since the ToC lists all the needed interdisciplinary topics for a study of this subject.
