As per history, it was built by Mughal emperor Shah Jahan in the memory of his Third wife Arjumand Banu Begum ie: Mumtaz mahal.
Many people have claimed over the years that tajmahal was built by hindu kings but was taken over by Mughals during their campaigns. Recently Subramanya swamy a famous personality known for bringing corrupt politicians to justice has also claimed it was a hindu temple which which was turned in to a grave for shajahans queen.
If you search online you will find numerous explanations for this.
A theory is that if you look at the architecture.. It is actually Hindu style of building than the mughal style.
Also there is a theory that no official records of shajahan undertaking the construction of tajmahal exist.
Just google it and you will find many interesting articles