We first realize Jack function of rectangular shapes. Then we introduce an iterative method to realize Jack functions of general shapes from those of rectangular shapes. As a byproduct, we prove some special cases of Richard P. Stanley's conjecture about the positivity of the Littlewood-Richardson coefficients of Jack functions.

Contents:
1. partitions and symmetric functions
2. Some history and questions about symmetric functions
3. Vertex operator realization of rectangular Jack functions
4. A special case of Stanley's conjecture and the realization of general Jack functions
5. Open questions