1. Introduction

2. Combinatorics of diagram

3. $q$-Whittaker polynomials

4. Some explicit values

5. Cauchy kernel and scalar product

6. $W$-expansion of Macdonald polynomials

7. Pieri rules

8. General up and down operators

9. $W$-positivity

10. Graded $\mathbb{S}_{n}$-modules for the Whittaker

11. Link to Science Fiction