Here we introduce the notion of a limit, look at its basic properties and cover the basic methods used in evaluating limits.

- Definition of a limit with some examples and terminology.
- Important examples:
alternating, arithmetic and geometric sequence; powers, factorial;
(1+1/ sine and cosine.*n*)^{n}; - Basic properties (operations, subsequence) and how they help with evaluating limits, including "algebra of limits" and "algebra of infinity".
- Limit and comparison, including the Squeeze theorem.
- Sequences and functions - some connections and differences.
- L'Hospital's rule (an intruder from theory of functions).
- Intuitive evaluation: Finding limits intuitively and the scale of powers.
- Stolz-Cesaro theorem.