Is a second marriage contract valid if the husband did not disclose that he was still married to his first wife?

I have a question about the marriage. Is a marriage legal when the man keep some important information for himself? When the woman knew about this, she didn't want to marrie him. It's about that the man didn't tell her, that he is still married with another woman.

Praise be to Allaah.

Firstly: 

The fuqaha’ (may Allaah have mercy on them) have listed some things which give either spouse the right to annul the marriage contract. Among these they mention annulment based on physical defects, in the sense that it is permissible for either the husband or the wife to request annulment of the marriage contract if one of them finds physical defects in the other. 

It says in al-Mawsoo’ah al-Fiqhiyyah (29/68): 

The fuqaha’ of the four madhhabs are agreed that it is permissible to separate the spouses on the grounds of physical defects. End quote. 

Not every physical defect that either spouse finds in the other means that it is permissible to annul the marriage, rather the guideline with regard to these faults is that it is that which prevents fulfilment of the purpose of marriage, such as physical pleasure, love, tranquillity, offspring and so on. 

Ibn Taymiyah said in al-Ikhtiyaaraat (p. 222): A woman may be rejected because of any physical defect that prevents full physical pleasure. End quote. 

Ibn al-Qayyim said: By analogy, every physical defect that puts one spouse off the other, and prevents fulfilment of the purpose of marriage such as compassion and love, results in giving the option of annulling the marriage. End quote. 

Shaykh Ibn ‘Uthaymeen said:  

The correct view is that there is a guideline on this issue, which is whatever people regard as a physical defect that prevents full physical pleasure,  this is a physical defect. Defects with regard to marriage are the same as defects with regard to financial transactions, because both are shortcomings that affect the contract. End quote. 

Secondly: 

The fact that a man is married to another woman is not a defect for which the marriage contract may be annulled, because the man has the right to marry a second, third and fourth wife, and she does not have the right to demand that the marriage be annulled if he is treating them all fairly. 

Shaykh Ibn Jibreen was asked: Is it essential for a marriage to be valid that the man should tell the woman whom he wants to marry that he has another wife, if she does not ask him about that? Are there any consequences if he denies it when asked? 

He replied: 

The man is not obliged to tell his wife or her family that he is already married if they do not ask him, but that is not usually concealed. Marriage cannot be done except after a period of researching and asking on the part of both spouses, to ensure that they are suited to one another. But it is not permissible to conceal anything. If one party lies and on the basis of that the other party decides to go ahead with the marriage, then the latter is given the choice. If he says that he is not married and he is lying, then she is allowed to have the marriage annulled. If they say that she is a virgin and that is not the case, then he has the choice of going ahead with the marriage or of leaving her. End quote. 

Fawaa’id wa Fataawa Tuhimm al-Mar’ah al-Muslimah, 114.