As far as I remember, Varian's book is aimed at second year undergraduates who are normally studying a micro 2 module (or something similar).
As a result, he does tend to assume some prior knowledge so it would be beneficial for you to plug the gaps in your knowledge (assuming you haven't) before you proceed with this book.
Even though you are studying mathematics, I will suggest resources in a way that will be accessible to mathematicians & non-mathematicians alike.
I would say that the prerequisites for intermediate micro are game theory & a micro 1 module. The prerequisite for a micro 1 module would be a sort of "Principles of Economics" module, where you encounter the very basics of economics.
This would be my plan for a two year "course" in micro & macro:
Micro and macro 1
- "Economics" by Sloman
- "Debunking Economics" by Keen (I would strongly suggest that you read this if you want to pursue your interest in economics)
- "Macroeconomics: Understanding the global Economy" by Miles,Scott & Breedon
- "Macroeconomics: A European Perspective" by Blanchard,Giavazzi
Before we proceed to "Year 2", ensure that you are comfortable with the following micro 1 topics:
1.Set theory & probability theory basics (Including bayes' theorem)
5.Choice under risk
6.Choice under uncertainty
7.Beliefs under uncertainty
Micro 2 prerequisites: Basic economics -> Micro 1
Macro 2 prerequisites: Understanding the global economy -> European perspective
"Economics of Development" by Thirlwall
"Macroeconomics" by Dornbusch et al.
"Macroeconomics" either the Blanchard or Mankiw version, take your pick.
And that's your basic contingent course of action... done.
However, I would like to add that if you want to understand the empirical side of economics, you should also study econometrics. In addition to this, I would stress that you study the history of economic thought. Learning economics without appreciating its historical and philosophical foundations leads to a half baked knowledge.
Now, to answer your specific question regarding the Varian book, this is how I would read it:
Technology (chapter 18)
Profit maximization (19)
Cost functions (20,21)
Firm supply (22,23)
Production & welfare (32,33)
Public goods (36)
Asymmetric information (37)
Hope that helps.