Under the Dissolution of Muslim Marriage Act, 1939, Muslim women can seek divorce on the following grounds:

1. Cruelty: If the husband has treated the wife with cruelty, whether mental or physical, she can seek divorce. This kind of cruelty should be proved by the Muslim woman for divorce.
2. Desertion: If the husband has deserted the wife for a continuous period of at least two years, she can seek divorce.
3. Impotency: If the husband is impotent at the time of the marriage and continues to be so, the wife can seek divorce.
4. Non-resumption of cohabitation: If the husband has obtained a decree of judicial separation and the wife has not resumed cohabitation with him for a period of one year or more after the passing of the decree, the wife can seek divorce.

The procedure for seeking divorce under the act involves filing a petition in a court of law. The petition must be filed in the court within whose territorial jurisdiction the husband or the wife has been residing for a period of not less than six months immediately preceding the presentation of the petition. The court will hear the evidence presented by both parties and make a decision based on the merits of the case.

It’s worth noting that the act is only applicable to Muslims in India, and it only covers dissolution of marriage. Other matters like maintenance, custody, and inheritance are governed by the personal laws of Muslims and the court’s decision is based on the principles of Muslim law.