If you're coming from a mathematics background, and you want to learn time series, it's hard to go wrong with a combination of:
- The Analysis of Time Series (Chatfield): introduction at the undergraduate level
- Fourier Analysis of Time Series (Bloomfield): introduction to Fourier methods at the undergraduate level
and after you've gone through those two and learned the basics, proceed to:
- Time Series: Theory and Methods (Brockwell & Davis): excellent high-level undergraduate / starting graduate-level book
- Spectral Analysis and Time Series (Priestley): excellent graduate-level text
and if you become interested in spectrum estimation, the best book I'm aware of is:
- Spectral Analysis for Physical Applications (Percival and Walden): more of an engineering flavour, but lots of great examples and carefully written algorithms that you can turn into code.
When I want to look up something I've seen before in classical time series methods, I mostly use Priestley. It's not an easy read by any means, but it's very well written, and you can go back to it and learn new things every time. Since you're coming from a mathematics background, you shouldn't have too much issue with any of the probabilistic notation, especially if you've had some measure theory. If I'm reviewing an algorithm for spectral methods, I use Percival & Walden: it's the only good book I'm aware of that covers modern spectrum estimation techniques without diverging too strongly into wavelets or time-frequency methods.
I would encourage you to stay away from focused books on econometrics or any area of time series where the focus is on one particular area, as nonstandard notation and terminology tends to develop within these subfields. If it's your first approach to time series, start with a couple of good general undergraduate books (1 and 2 are decent, and have lots of examples that you can work through on your own with R). Only after you know the basics should you venture into the world of specific subfields and read books there.