Is it permissible for a woman to marry a man who does not pray, and is it considered adultery?

It is not permissible to marry someone who completely abandons prayer, because he is considered a disbeliever by a group of scholars, including Imam Ahmad. In this case, marriage to him would be fornication and adultery. Even if he is not considered a disbeliever, his action is a major sin, and there is fear for the children from his influence, and fear for the wife that she might be influenced by him, or that he might mistreat her in the future. Therefore, the questioner should leave him, for whoever leaves something for the sake of Allah, Allah will compensate him with something better.