Let $f : X \to X$ be a continuous map of compact closed manifold. A point $x \in X$ is called a periodic point of $f$ of period $n$ if there exists $n \in\mathbb{N}$ such that $f^n(x) = x$. We will present a survey of methods based on the classical Lefschetz and Nielsen theories which estimate (from below) the number periodic points of period n and describe appearing minimal periods. By their constructions these methods give invariants which are preserved by a homotopy of map. Consequently they are rough but on the other side stable, i.e. these invariants are preserved by a deformation in particular by a small perturbation of map. A combination of these methods with another assumptions on $f$, as $C^1$-smoothness, symmetry, analyticity let us to improve essentially results.
