Second marriage without divorcing the first wife is illegal and is considered an offence under different laws.
Under section 5 of The Hindu Marriage Act talks about the conditions which are required to consider marriage as valid. The conditions in the context of second marriage are that at the time of marriage, the husband or wife of the parties should not be living or should not be alive or the first marriage had been dissolved at the time of second marriage otherwise second marriage will be considered as void under Section 11 of The Hindu Marriage Act.
Under Section 17 of the Act, the punishment for bigamy is given, which states that if a person commits bigamy it will be dealt with under section 494 and 495 of the Indian Penal Code and it will be considered a criminal offence.
Under Section 494 of the Indian Penal Code states that if a person marries while his/her husband/wife is alive at the time of marriage it will consider as bigamy, which is a punishable offence. If the husband/wife thinks they can also file a complaint under Section 415 of the Indian Penal Code which talks about cheating but this section only applies when the person doesn't know that the other party is married.
For an offence of bigamy to have been committed the following ingredients are required (i) the accused must have contracted first marriage (ii) he/she must have married again (iii) the first marriage must be subsisting (that is no divorce has taken place) (iv) the first spouse must be living, Pashaura Singh v. State of Punjab, (2010) 11 SCC 749.
Only a person aggrieved by his or her spouse contracting the second marriage can file the complaint.