How do traders process and learn from market information, what trading strategies should they use, and how does learning affect the market? This paper proposes a learning model of an artificial limit order market with asymmetric information to address these issues. Using a genetic algorithm as a learning mechanism, we show that learning, in particular the learning from uninformed traders, improves market informational efficiency and has a significant impact on the stylized facts of limit order markets, order submission, liquidity supply and consumption, the hump shaped order book near the quote, and the bid-ask spread. Moreover, the learning affects the evolution process of the trading strategies for all traders. The model provides some insights into market efficiency, the interaction of traders, the dynamics of limit order books, and the evolution of trading strategies.