Here we introduce the notion of a series of real numbers and look at its important properties. The central question - convergence - is introduced here, but the most important practical results are found in Theory - Testing convergence.

- Introduction: series of real numbers, convergence, reindexing.
- Basic properties: operations, summing over subsets and reordering, convergence.
- Important examples: geometric
series, series with powers (
*p*-series). - Summing up series: geometric, telescopic, Taylor series.
- Approximating series, error of approximation.
- Absolute convergence.