**MSC:**- 06A06 Partial order, general
- 05D05 Extremal set theory

of the classical Kruskal-Katona theorem for finite sets.

These posets are of great importance in many branches of

combinatorics but have numerous applications.

We survey mostly new and also some old results on Macaulay posets,

where the intension is to present them as pieces of a general theory.

In particular, the classical examples of Macaulay posets are

included as well as new ones. Emphasis is also put on construction

of Macaulay posets, and their relations to other disrete

optimization problems.