PocketChess is a great free-distribution chess game ideal for improving and expanding your knowledge of the game and strategic skills.
Here are some of its main features:
* Play against the computer or a friend. * Simple and intuitive user interface * Choose from 8 levels of skill. * Export to PGN * Save & load games * Opening move libary
All in all, this is a well designed, simple and free way of practising your Chess and improving your strategic thinking.